Exterminate
late Middle English (in the sense ‘drive out’): from Latin exterminat- ‘driven out’, from the verb exterminare, from ex- ‘out’ + terminus ‘boundary’. The sense ‘destroy’ (mid 16th century) comes from the Latin of the Vulgate.
wiktionary
From Latin exterminātus, perfect passive participle of exterminō, itself from ex- + terminō(“I finish, close, end”) (from terminus(“limit, end”)).
etymonline
exterminate (v.)
1540s, "drive away," from Latin exterminatus, past participle of exterminare "drive out, expel, put aside, drive beyond boundaries," also, in Late Latin "destroy," from phrase ex termine "beyond the boundary," from ex "out of" (see ex-) + termine, ablative of termen "boundary, limit, end" (see terminus).
Meaning "destroy utterly" is from 1640s in English, a sense found in equivalent words in French and in the Vulgate; earlier in this sense was extermine (mid-15c.). Related: Exterminated; exterminating.