The Collaborative International Dictionary of English v.0.48:

Stupefy \Stu"pe*fy\, v. t. [imp. & p. p. Stupefied; p. pr. &
   vb. n. Stupefying.] [F. stup['e]fier, fr. L. stupere to be
   stupefied + ficare (in comp.) to make, akin to facere. See
   Stupid, Fact, and cf. Stupefacient.] [Written also
   stupify, especially in England.]
   1. To make stupid; to make dull; to blunt the faculty of
      perception or understanding in; to deprive of sensibility;
      to make torpid.
      [1913 Webster]

            The fumes of drink discompose and stupefy the brain.
                                                  --South.
      [1913 Webster]

   2. To deprive of material mobility. [Obs.]
      [1913 Webster]

            It is not malleable; but yet is not fluent, but
            stupefied.                            --Bacon.
      [1913 Webster]

WordNet (r) 3.0 (2006):

stupefy
    v 1: make dull or stupid or muddle with drunkenness or
         infatuation [syn: besot, stupefy]
    2: 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]
    3: make senseless or dizzy by or as if by a blow; "stun fish"
       [syn: stun, stupefy]