The Collaborative International Dictionary of English v.0.48:

Exterminate \Ex*ter"mi*nate\, v. t. [imp. & p. p.
   Exterminated; p. pr. & vb. n. Exterminating.] [L.
   exterminatus, p. p. of exterminare to abolish, destroy, drive
   out or away; ex out + terminus boundary, limit. See Term.]
   1. To drive out or away; to expel.
      [1913 Webster]

            They deposed, exterminated, and deprived him of
            communion.                            --Barrow.
      [1913 Webster]

   2. To destroy utterly; to cut off; to extirpate; to
      annihilate; to root out; as, to exterminate a colony, a
      tribe, or a nation; to exterminate error or vice.
      [1913 Webster]

            To explode and exterminate rank atheism. --Bentley.
      [1913 Webster]

   3. (Math.) To eliminate, as unknown quantities. [R.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

exterminate
    v 1: kill en masse; kill on a large scale; kill many; "Hitler
         wanted to exterminate the Jews, Gypsies, Communists, and
         homosexuals of Europe" [syn: exterminate, kill off]
    2: destroy completely, as if down to the roots; "the vestiges of
       political democracy were soon uprooted" "root out corruption"
       [syn: uproot, eradicate, extirpate, root out,
       exterminate]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "exterminate":
   abate, abolish, annihilate, bereave of life, blot out, bump off,
   butcher, carry away, carry off, cast off, chloroform, cut down,
   cut off, cut out, deprive of life, deracinate, destroy, dispatch,
   dispel, dispose of, do away with, do for, do to death, eliminate,
   end, eradicate, execute, extinguish, extirpate, finish, finish off,
   fling off, get rid of, immolate, kill, launch into eternity,
   liquidate, lynch, make away with, martyr, martyrize, massacre,
   murder, obliterate, poison, purge, put away, put down,
   put to death, put to sleep, remove, remove from life, root out,
   root up, rub out, sacrifice, shake off, shoo, slaughter, slay,
   stamp out, starve, sweep away, take life, take off, terminate,
   throw away, throw off, uproot, waste, weed out, wipe out