WordNet (r) 3.0 (2006):

clear up
    v 1: make clear and (more) comprehensible; "clarify the mystery
         surrounding her death" [syn: clarify, clear up,
         elucidate] [ant: obfuscate]
    2: finish a task completely; "I finally got through this
       homework assignment" [syn: get through, wrap up, finish
       off, mop up, polish off, clear up, finish up]
    3: free (the throat) by making a rasping sound; "Clear the
       throat" [syn: clear, clear up]
    4: become clear; "The sky cleared after the storm" [syn: clear
       up, clear, light up, brighten] [ant: cloud,
       overcast]
    5: make free from confusion or ambiguity; make clear; "Could you
       clarify these remarks?"; "Clear up the question of who is at
       fault" [syn: clear, clear up, shed light on,
       crystallize, crystallise, crystalize, crystalise,
       straighten out, sort out, enlighten, illuminate,
       elucidate]

Moby Thesaurus II by Grady Ward, 1.0:

131 Moby Thesaurus words for "clear up":
   account for, allegorize, answer, ascertain, assure, bottom,
   certify, cinch, cipher, clarify, clean up, clear, clear the decks,
   clinch, crack, debug, decide, decipher, decode, demonstrate,
   demythologize, determine, disembroil, disentangle, disintricate,
   disinvolve, dismiss all doubt, dissolve, divine, do, dope,
   dope out, elucidate, enlighten, ensure, establish, euhemerize,
   exemplify, explain, explain away, explicate, exposit, expound,
   fathom, figure out, find out, find the answer, find the solution,
   fix, fix up, get, get at, get right, give reason for,
   give the meaning, groom, guess, guess right, have it, hit it,
   illuminate, illustrate, insure, interpret, make certain,
   make clear, make no doubt, make no mistake, make out, make plain,
   make sure, make sure of, nail down, neaten, open the lock, plumb,
   police, police up, popularize, psych, psych out, put in trim,
   puzzle out, rationalize, ravel, ravel out, reassure,
   remove all doubt, resolve, riddle, see that, see to it,
   set at rest, settle, shed light upon, show, show how, show the way,
   simplify, solve, sort out, spell out, spruce, spruce up,
   straighten up, throw light upon, tidy, tidy up, trig up, trim,
   trim up, unbraid, unclutter, uncoil, undo, unfold, unknot, unlock,
   unmix, unravel, unriddle, unscramble, unsnarl, untangle, unthread,
   untwine, untwist, unweave, unwind, work, work out