<?xml version="1.0" encoding="us-ascii"?>
<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2021-03-01T14:53:23.0748520+00:00 -->
<!-- Version            : 5.0.1.571 -->
<!-- Package ID         : 4deb668a9fed4213bf062e3f81b7336c -->
<!-- Copyright (c) 2021 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="axsm_TwoThousandEighteenRegisteredDirectOfferingMember" name="TwoThousandEighteenRegisteredDirectOfferingMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_DecemberTwoThousandNineteenSalesAgreementMember" name="DecemberTwoThousandNineteenSalesAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_UnderwrittenPublicOfferingMember" name="UnderwrittenPublicOfferingMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_TwoThousandNineteenShelfRegistrationMember" name="TwoThousandNineteenShelfRegistrationMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_TwoThousandThirteenEquityCompensationPlanMember" name="TwoThousandThirteenEquityCompensationPlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_TwoThousandFifteenEquityCompensationPlanMember" name="TwoThousandFifteenEquityCompensationPlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_StockIssuedDuringPeriodValueNewIssuesNet" name="StockIssuedDuringPeriodValueNewIssuesNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="axsm_WarrantExercisePrice" name="WarrantExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantUtilized" name="WarrantUtilized" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="axsm_CommonStockSalesAgreementSharesUnsoldAmount" name="CommonStockSalesAgreementSharesUnsoldAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="axsm_EquityInstrumentVotingRightsPerShare" name="EquityInstrumentVotingRightsPerShare" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_AllocatedShareBasedCompensationExpenseRelatedToPlanCancelled" name="AllocatedShareBasedCompensationExpenseRelatedToPlanCancelled" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="axsm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsCancelledInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsCancelledInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsCancelledInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsCancelledInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsCancelledInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsCancelledInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsCancelledWeightedAverageGrantDateFairValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsCancelledWeightedAverageGrantDateFairValue" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ConvertibleNotesPayableTrancheOneMember" name="ConvertibleNotesPayableTrancheOneMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2013Member" name="Warrants2013Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_WarrantsIssuedInPeriod" name="WarrantsIssuedInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantsExercisedInPeriod" name="WarrantsExercisedInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantsExpiredInPeriod" name="WarrantsExpiredInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantsIssuedInPeriodWeightedAverageExercisePrice" name="WarrantsIssuedInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantsExercisedInPeriodWeightedAverageExercisePrice" name="WarrantsExercisedInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_WarrantsExpiredInPeriodWeightedAverageExercisePrice" name="WarrantsExpiredInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_DebtInstrumentAggregateAmountPercentage" name="DebtInstrumentAggregateAmountPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ClassOfWarrantsOrRightsWeightedAveragePriceTradingDays" name="ClassOfWarrantsOrRightsWeightedAveragePriceTradingDays" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_ClassOfWarrantOrRightTerm" name="ClassOfWarrantOrRightTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_NumberOfWarrantsExercisable" name="NumberOfWarrantsExercisable" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="axsm_ClassOfWarrantOrRightMandatoryConversionPricePremiumPercentage" name="ClassOfWarrantOrRightMandatoryConversionPricePremiumPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_Warrants2020Member" name="Warrants2020Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2019Member" name="Warrants2019Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2018Member" name="Warrants2018Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2017Member" name="Warrants2017Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2016Member" name="Warrants2016Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Warrants2014Member" name="Warrants2014Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_ConsecutiveTradingDays" name="ConsecutiveTradingDays" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_InitialCashPaymentPerCollaborationAgreement" name="InitialCashPaymentPerCollaborationAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="axsm_SharePriceFairValue" name="SharePriceFairValue" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="axsm_CommonStockFairValue" name="CommonStockFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="axsm_PfizerIncMember" name="PfizerIncMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_Axs05Member" name="Axs05Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="axsm_CollaborationArrangementFuturePotentialPayments" name="CollaborationArrangementFuturePotentialPayments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="axsm_NumberOfLicenseAgreements" name="NumberOfLicenseAgreements" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_LicenseAgreementRoyaltyDuePercentageOfNetSales" name="LicenseAgreementRoyaltyDuePercentageOfNetSales" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_LicenseAgreementRoyaltyDueMaximumReductionPercentageAsResultOfRequiredPaymentsToThirdParties" name="LicenseAgreementRoyaltyDueMaximumReductionPercentageAsResultOfRequiredPaymentsToThirdParties" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_LicenseAgreementTerm" name="LicenseAgreementTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_OperatingLossCarryforwardsExpirationYear" name="OperatingLossCarryforwardsExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_DeferredTaxAssetsInterestExpense" name="DeferredTaxAssetsInterestExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="axsm_DeferredTaxAssetsCharitableContribution" name="DeferredTaxAssetsCharitableContribution" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="axsm_DeferredTaxAssetsLeasingArrangements" name="DeferredTaxAssetsLeasingArrangements" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="axsm_EffectiveIncomeTaxRateReconciliationPermanentDifferencesPercent" name="EffectiveIncomeTaxRateReconciliationPermanentDifferencesPercent" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_TaxCutsAndJobsActNetOperatingLossCarryoversAndCarryBacksOffsetPercentage" name="TaxCutsAndJobsActNetOperatingLossCarryoversAndCarryBacksOffsetPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_CARESActNetOperatingLossCarrybackPeriod" name="CARESActNetOperatingLossCarrybackPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="axsm_BeneficialOwnershipPercentage" name="BeneficialOwnershipPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
</xsd:schema>
