The Collaborative International Dictionary of English v.0.48:

Untwist \Un*twist"\, v. t. [1st pref. un- + twist.]
   [1913 Webster]
   1. To separate and open, as twisted threads; to turn back, as
      that which is twisted; to untwine.
      [1913 Webster]

            If one of the twines of the twist do untwist,
            The twine that untwisteth, untwisteth the twist.
                                                  --Wallis.
      [1913 Webster]

   2. To untie; to open; to disentangle. --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

untwist
    v 1: cause to become untwisted [ant: distort, twine,
         twist]

Moby Thesaurus II by Grady Ward, 1.0:

59 Moby Thesaurus words for "untwist":
   answer, bottom, clarify, clear up, crack, debug, decipher, decode,
   disembroil, disentangle, disintricate, disinvolve, divine, do,
   dope, dope out, explain, fathom, figure out, find out,
   find the answer, find the solution, get, get right, guess,
   guess right, have it, hit it, interpret, make out, open the lock,
   plumb, psych, psych out, puzzle out, ravel, ravel out, resolve,
   riddle, solve, sort out, unbraid, unclutter, uncoil, undo, unknot,
   unlock, unmix, unravel, unriddle, unscramble, unsnarl, untangle,
   unthread, untwine, unweave, unwind, work, work out