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):

mystifying
    adj 1: of an obscure nature; "the new insurance policy is
           written without cryptic or mysterious terms"; "a deep
           dark secret"; "the inscrutable workings of Providence";
           "in its mysterious past it encompasses all the dim
           origins of life"- Rachel Carson; "rituals totally
           mystifying to visitors from other lands" [syn: cryptic,
           cryptical, deep, inscrutable, mysterious,
           mystifying]

Moby Thesaurus II by Grady Ward, 1.0:

20 Moby Thesaurus words for "mystifying":
   baffling, bewildering, bothering, confounding, confusing, dark,
   discomposing, disconcerting, dismaying, distracting, disturbing,
   embarrassing, enigmatic, intricate, mysterious, perplexing,
   perturbing, problematic, puzzling, upsetting