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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001253689</issuerCik>
        <issuerName>GLYCOMIMETICS INC</issuerName>
        <issuerTradingSymbol>GLYC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340097</rptOwnerCik>
            <rptOwnerName>Invus Public Equities, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>750 LEXINGTON AVENUE 30TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001218180</rptOwnerCik>
            <rptOwnerName>Artal International S.C.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001522131</rptOwnerCik>
            <rptOwnerName>Artal International Management S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001053906</rptOwnerCik>
            <rptOwnerName>Artal Group S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001283968</rptOwnerCik>
            <rptOwnerName>Westend S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001841311</rptOwnerCik>
            <rptOwnerName>Wittouck Amaury</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001460840</rptOwnerCik>
            <rptOwnerName>Stichting Administratiekantoor Westend</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CLAUDE DEBUSSYLAAN, 46</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>AMSTERDAM</rptOwnerCity>
            <rptOwnerState>P7</rptOwnerState>
            <rptOwnerZipCode>1082 MD</rptOwnerZipCode>
            <rptOwnerStateDescription>NETHERLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340096</rptOwnerCik>
            <rptOwnerName>Invus Public Equities Advisors, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>750 LEXINGTON AVENUE 30TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>11451</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.2419</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6573798</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Common Stock is held directly by Invus Public Equities, L.P. The general partner of Invus Public Equities, L.P. is Invus Public Equities Advisors, LLC. The Geneva branch of Artal International S.C.A. is the managing member of Invus Public Equities Advisors, LLC. The managing partner of Artal International S.C.A. is Artal International Management S.A., which is a wholly owned subsidiary of Artal Group S.A. Westend S.A. is the parent company of Artal Group, S.A., and the majority stockholder of Westend S.A. is Stichting Administratiekantoor Westend (&quot;Stichting&quot;).</footnote>
        <footnote id="F2">(Continued from Footnote 1) Mr. Amaury Wittouck is the sole member of the board of Stichting. Each of the Reporting Persons, other than Invus Public Equities L.P., disclaims beneficial ownership of the securities held by the other Reporting Persons, except to the extent of such reporting person's pecuniary interest therein, and, pursuant to Rule 16a-1(a)(4) under the Exchange Act, each of the reporting persons (other than to the extent it directly holds securities reported herein) states that the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all of the reported securities for purposes of Section 16 of the Exchange Act or for any other purpose.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $3.07 to $3.30 per share, inclusive. The Reporting Persons undertake to provide to GlycoMimetics, Inc., any security holder of GlycoMimetics, Inc., or the staff of the SEC, upon request, full information regarding the number of shares purchased at each separate price within the range set forth in this footnote.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Invus Public Equities, L.P., By: Invus Public Equities Advisors, LLC, its General Partner, By: /s/ Raymond Debbane, President</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Invus Public Equities Advisors, LLC, By: /s/ Raymond Debbane, President</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal International S.C.A., By: Artal International Management S.A., its Managing Partner, By: /s/ Anne Goffard, Managing Director</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal International Management S.A., By: /s/ Anne Goffard, Managing Director</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal Group S.A., By: /s/ Anne Goffard, Authorized Person</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Westend S.A., By: /s/ Anne Goffard, Managing Director</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Stichting Administratiekantoor Westend, By: /s/ Amaury Wittouck, Sole Member of the Board</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Amaury Wittouck</signatureName>
        <signatureDate>2023-02-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
