Synonyms for Exterminate:

n.

bump off, take someone's life. exterminate (noun)
eradicate, uproot, extirpate, kill off.

v.

contact (verb)
kill off.
destroy (verb)
devastate, destroy, decimate, pulverize, demolish, flatten, wreck, mow down, smash, extirpate, atomize, abolish, level, eradicate, bulldoze, disintegrate, rip to shreds, vaporize, desolate, tear down, annihilate, raze, dismantle, lay waste.
kill (verb)
decimate, put to sleep, smother, execute, put an end to, destroy, purge, hang, abolish, assassinate, extirpate, slay, remove, asphyxiate, sacrifice, slaughter, massacre, chill, eradicate, butcher, rub out, dispatch, blot out, do away with, drown, eliminate, ice, suffocate, snuff, smite, erase, liquidate, annihilate, do in, strangle.

Other synonyms:

bump off, hunt out. hunt, poach, rub out. cull. erase. bag. put down. destroy
decimate, lay waste.
kill
slay, snuff.
zap
vaporize.
Other relevant words:
cull, uproot, make, clear, hunt, make an end of, poach, blot out, put an end to, bump off, snuff out, erase, bag, rub out.

Usage examples for exterminate

  1. For Agesilaus, while attempting to enslave Thebes and exterminate Messene, the latter, his country's ancient associate, and Thebes, the mother- city of his own royal house, almost lost Sparta itself, and did really lose the government of Greece; whereas Pompey gave cities to those of the pirates who were willing to change their manner of life; and when it was in his power to lead Tigranes, king of Armenia, in triumph, he chose rather to make him a confederate of the Romans, saying, that a single day was worth less than all future time. – Plutarch-Lives-of-the-noble-Grecians-and-Romans by Clough, Arthur Hugh
  2. The Scotch- Irish had worked themselves up into a strange belief that these small remnants were sending information, arms, and ammunition to the western tribes; and they seemed to think that it was more important to exterminate these little communities than to go with such expeditions as Bouquet's to the West. – The Quaker Colonies A Chronicle of the Proprietors of the Delaware, Volume 8 in The Chronicles Of America Series by Sydney G. Fisher
  3. Can you exterminate twenty Germans in a fortified back- parlour by a single thrust with a bayonet? – The First Hundred Thousand by Ian Hay