The Collaborative International Dictionary of English v.0.48:

Cup \Cup\, v. t. [imp. & p. p. Cupped (k[u^]pt); p. pr. & vb.
   n. Cupping.]
   1. To supply with cups of wine. [R.]
      [1913 Webster]

            Cup us, till the world go round.      --Shak.
      [1913 Webster]

   2. (Surg.) To apply a cupping apparatus to; to subject to the
      operation of cupping. See Cupping.
      [1913 Webster]

   3. (Mech.) To make concave or in the form of a cup; as, to
      cup the end of a screw.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Cupping \Cup"ping\ (k?p"p?ng), n. (Med.)
   The operation of drawing blood to or from the surface of the
   person by forming a partial vacuum over the spot. Also,
   sometimes, a similar operation for drawing pus from an
   abscess.
   [1913 Webster]

   Cupping glass, a glass cup in which a partial vacuum is
      produced by heat, in the process of cupping.

   Dry cupping, the application of a cupping instrument
      without scarification, to draw blood to the surface,
      produce counter irritation, etc.

   Wet cupping, the operation of drawing blood by the
      application of a cupping instrument after scarification.
      [1913 Webster]

WordNet (r) 3.0 (2006):

cupping
    n 1: a treatment in which evacuated cups are applied to the skin
         to draw blood through the surface

Moby Thesaurus II by Grady Ward, 1.0:

19 Moby Thesaurus words for "cupping":
   aspiration, bleeding, bloodletting, broaching, drafting, drainage,
   draining, drawing, emptying, leeching, milking, phlebotomy,
   pipetting, pumping, siphoning, sucking, suction, tapping,
   venesection