  In this paper, we consider the discrete deformation of the discrete space
curves with constant torsion described by the discrete mKdV or the discrete
sine-Gordon equations, and show that it is formulated as the torsion-preserving
equidistant deformation on the osculating plane which satisfies the
isoperimetric condition. The curve is reconstructed from the deformation data
by using the Sym-Tafel formula. The isoperimetric equidistant deformation of
the space curves does not preserve the torsion in general. However, it is
possible to construct the torsion-preserving deformation by tuning the
deformation parameters. Further, it is also possible to make an arbitrary
choice of the deformation described by the discrete mKdV equation or by the
discrete sine-Gordon equation at each step. We finally show that the discrete
deformation of discrete space curves yields the discrete K-surfaces.
