Classical trajectory calculations have been performed to investigate the collision-induced dissociation (CID) of the CH3SH+ cation with Ar atoms. A new intramolecular potential energy surface for the CH3SH+ cation is evaluated by interpolation of 3000 ab initio data points calculated at the MP2/6-311G(d,p) level of theory. The new potential energy surface includes seven accessible dissociation channels of the cation. The present QCT calculations show that migration of hydrogen atoms, leading to the rearrangement CH3SH+<-> CH2SH2+, is significant at the collision energies considered (6.5-34.7 eV) and that the formation of CH3+, CH3S+, and CH2+ cations takes place primarily by a "shattering" mechanism in which the products are formed just after the collision. The theoretical product abundances are found to be in qualitative agreement with the experimental data. However, at high collision energies, the calculated total cross sections for the formation of CH3+ and CH2SH+ cations are noticeably larger than the experimental determinations. Several features of the dynamics of the CID processes are discussed.