<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-06-13</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001579428</issuerCik>
        <issuerName>Axsome Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>AXSM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001934008</rptOwnerCik>
            <rptOwnerName>Murdock Hunter R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AXSOME THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>22 CORTLANDT ST, 16TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>32.55</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-12-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.91</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-03-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>52383</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>22254</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>27698</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option was granted on December 13, 2021. 25% of the option vests on the one (1) year anniversary of the date of grant with the remaining 75% to vest in equal increments on a quarterly basis over a four (4) year period, until fully vested.</footnote>
        <footnote id="F2">The option was granted on March 4, 2022, and vests in equal increments on a quarterly basis over a four (4) year period, until fully vested.</footnote>
        <footnote id="F3">The restricted stock units (&quot;RSUs&quot;) were granted on December 13, 2021. 25% of the RSUs will vest on the one (1) year anniversary of the date of grant. The remaining RSUs will vest in three substantially equal annual installments, such that the RSUs will be fully vested on December 13, 2025. Vested shares will be delivered to the reporting person upon the earlier of (i) the closing of a Change in Control (as defined in the Issuer's Amended and Restated 2015 Omnibus Incentive Compensation Plan (the &quot;Plan&quot;)), (ii) separation of service from the Issuer (including termination with or without Cause (as defined in the Plan), or termination due to death or disability) of the reporting person or (iii) seven (7) years from the date of grant.</footnote>
        <footnote id="F4">Each RSU represents a contingent right to receive one share of the Issuer's common stock.</footnote>
        <footnote id="F5">The RSUs were granted on March 4, 2022. 25% of the RSUs will vest on the one (1) year anniversary of the date of grant. The remaining RSUs will vest in three substantially equal annual installments, such that the RSUs will be fully vested on March 4, 2026. Vested shares will be delivered to the reporting person upon the earlier of (i) the closing of a Change in Control (as defined in the Plan), (ii) the reporting person's separation of service from the Issuer (including termination with or without Cause (as defined in the Plan), or termination due to death or disability), or (iii) seven (7) years from the date of grant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Hunter Murdock</signatureName>
        <signatureDate>2022-06-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
