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]