'apocopate' (base of 'apocopating') ultimately originates from Greek, specifically the word 'apokopē' (ἀποκοπή), where 'apo-' meant 'away' and 'koptein' (root 'kop-') meant 'to cut'.

'apokopē' passed into Latin and later Medieval/Modern scholarly Latin and French as 'apocope' and was adopted into English as 'apocope' (noun); the verb 'apocopate' was later formed in Modern English from the noun plus the verb-forming suffix '-ate', yielding the modern English verb 'apocopate' and its forms such as 'apocopating'.

Originally it meant 'a cutting off' (literally 'cutting away'), and over time it came to refer specifically to the linguistic loss of a word's final sound or syllable; the verb now means to cause or undergo that loss.