The Collaborative International Dictionary of English v.0.48:

Mystify \Mys"ti*fy\, v. t. [imp. & p. p. Mystified; p. pr. &
   vb. n. Mystifying.] [F. mystifier, fr. Gr. ? + L. -ficare
   (in comp.) to make. See 1st Mystery, and -fy.]
   1. To involve in mystery; to make obscure or difficult to
      understand; as, to mystify a passage of Scripture.
      [1913 Webster]

   2. To perplex the mind of; to puzzle; to impose upon the
      credulity of; to baffle; as, to mystify an opponent.
      [1913 Webster]

            He took undue advantage of his credulity and
            mystified him exceedingly.            --Ld.
                                                  Campbell.
      [1913 Webster]

WordNet (r) 3.0 (2006):

mystify
    v 1: be a mystery or bewildering to; "This beats me!"; "Got me--
         I don't know the answer!"; "a vexing problem"; "This
         question really stuck me" [syn: perplex, vex, stick,
         get, puzzle, mystify, baffle, beat, pose,
         bewilder, flummox, stupefy, nonplus, gravel,
         amaze, dumbfound]
    2: make mysterious; "mystify the story" [ant: demystify]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "mystify":
   addle, amaze, around the bush, baffle, bamboozle, beat, beat about,
   beg the question, bewilder, bicker, boggle, buffalo, cavil,
   choplogic, complicate, confound, confuse, corrupt, daze, dodge,
   equivocate, evade, evade the issue, fence, floor, flummox, fool,
   fuddle, garble, get, hedge, hoax, humbug, jumble, keep in suspense,
   lick, make unintelligible, maze, misadvise, misdirect, miseducate,
   misguide, misinform, misinstruct, mislead, misteach, mix up,
   muddle, nitpick, nonplus, obfuscate, obscure, palter, parry,
   perplex, pervert, pick nits, prevaricate, pussyfoot, puzzle,
   quibble, scramble, shadow, shift, shuffle, shy, sidestep,
   split hairs, stick, stump, tergiversate, throw