The Collaborative International Dictionary of English v.0.48:

Eliminate \E*lim"i*nate\, v. t. [imp. & p. p. Eliminated; p.
   pr. & vb. n. Eliminating.] [L. eliminatus, p. p. of
   eliminare; e out + limen threshold; prob. akin to limes
   boundary. See Limit.]
   1. To put out of doors; to expel; to discharge; to release;
      to set at liberty.
      [1913 Webster]

            Eliminate my spirit, give it range
            Through provinces of thought yet unexplored.
                                                  --Young.
      [1913 Webster]

   2. (Alg.) To cause to disappear from an equation; as, to
      eliminate an unknown quantity.
      [1913 Webster]

   3. To set aside as unimportant in a process of inductive
      inquiry; to leave out of consideration.
      [1913 Webster]

            Eliminate errors that have been gathering and
            accumulating.                         --Lowth.
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   4. To obtain by separating, as from foreign matters; to
      deduce; as, to eliminate an idea or a conclusion. [Recent,
      and not well authorized]
      [1913 Webster]

   5. (Physiol.) To separate; to expel from the system; to
      excrete; as, the kidneys eliminate urea, the lungs
      carbonic acid; to eliminate poison from the system.
      [1913 Webster]

WordNet (r) 3.0 (2006):

eliminate
    v 1: terminate, end, or take out; "Let's eliminate the course on
         Akkadian hieroglyphics"; "Socialism extinguished these
         archaic customs"; "eliminate my debts" [syn: extinguish,
         eliminate, get rid of, do away with]
    2: do away with [syn: obviate, rid of, eliminate] [ant:
       ask, call for, demand, involve, necessitate,
       need, postulate, require, take]
    3: kill in large numbers; "the plague wiped out an entire
       population" [syn: eliminate, annihilate, extinguish,
       eradicate, wipe out, decimate, carry off]
    4: dismiss from consideration or a contest; "John was ruled out
       as a possible suspect because he had a strong alibi"; "This
       possibility can be eliminated from our consideration" [syn:
       rule out, eliminate, winnow out, reject]
    5: eliminate from the body; "Pass a kidney stone" [syn:
       excrete, egest, eliminate, pass]
    6: remove from a contest or race; "The cyclist has eliminated
       all the competitors in the race"
    7: remove (an unknown variable) from two or more equations

Moby Thesaurus II by Grady Ward, 1.0:

143 Moby Thesaurus words for "eliminate":
   abandon, abscind, abstract, amputate, annihilate, assassinate, ban,
   bar, bate, blow, blow out, bob, cast, cast aside, cast away,
   cast off, cast out, chuck, clean out, clear, clear away, clear off,
   clear out, clear the decks, clip, count out, crop, cull, cut,
   cut away, cut off, cut out, debar, deep-six, defecate, delete,
   deplete, deport, deracinate, discard, discharge, dismiss, dispel,
   dispose of, ditch, do away with, dock, drain, dump, effuse, egest,
   eighty-six, eject, elide, emit, empty, empty out, enucleate,
   eradicate, erase, evacuate, evict, except, excise, exclude,
   excrete, exhaust, exile, expatriate, expel, expunge, exterminate,
   extinguish, extirpate, extravasate, exudate, exude, fling off,
   freeze out, get quit of, get rid of, get shut of, give away,
   give off, isolate, jettison, jilt, knock off, liquidate, lop,
   murder, mutilate, nip, oust, outlaw, pare, part with, pass, peel,
   pick out, prune, purge, reject, remove, root out, root up,
   rule out, scour out, secrete, set apart, set aside, shake off,
   shave, shear, shoo, shut out, slough, stamp out, strike off,
   strike out, strip, strip off, suspend, sweep away, sweep out,
   take off, take out, throw away, throw off, throw out, throw over,
   throw overboard, toss overboard, transude, truncate, unclog,
   unfoul, uproot, vent, void, weed out, weep, wipe out