exterminate (v.) Look up exterminate at Dictionary.com
1540s, "drive away," from Latin exterminatus, past participle of exterminare "drive out, expel, 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.