'sex-drive-suppressing' is a modern English compound formed from 'sex-drive' (itself from 'sex' + 'drive') and the present participle 'suppressing' of the verb 'suppress'. 'sex' originates from Latin 'sexus' meaning 'sex, gender'; 'drive' traces to Old English 'drīfan' meaning 'to drive, to propel'; 'suppress' originates from Latin 'supprimere' (from 'sub-' meaning 'under' + 'premere' meaning 'to press').

'suppress' entered English via Latin 'supprimere' and Old French forms (e.g. 'supprimer'), later becoming Middle English and modern English 'suppress'. 'sex' comes from Latin 'sexus' and passed into English through Medieval/early modern usage. The compound 'sex-drive' is a 20th-century coinage combining 'sex' and 'drive' (in the psychological sense), and 'sex-drive-suppressing' is formed by attaching the present participle 'suppressing' to that compound.

Individually, 'suppress' originally meant 'to press down' and developed the sense 'to restrain or put an end to'; 'sex-drive-suppressing' specifically means 'producing the effect of restraining sexual desire', a specialization of the general sense of 'suppress'.