We present a spectroscopic survey of the rich X-ray-selected galaxy cluster CL 1358+6245 at z=0.328. When our 173 new multislit spectra of cluster galaxies are combined with data from the literature, we produce a catalog of 232 cluster members in a region 10'x11' (3.5Mpcx3.8Mpc) surrounding the brightest cluster galaxy. These data are used to study the structure and dynamics of the cluster and to examine the radial and velocity distributions as a function of spectral type. We classify the spectral types of the cluster members according to the strengths of the Balmer absorption lines (H{delta}, H{gamma}, and H{beta}) and the [O II] 3727{AA} emission line.