In this paper, the S(3P)+HD→SD+H and SH+D reactions are studied by means of quantum wave packet (QMWP) and quasi-classical trajectory (QCT) methods on a new ab initio 3A" potential energy surface. The reactive probabilities, integral cross sections, intra-molecular isotope parameters and product rotational alignment parameters for both reactive channels are calculated for collision energies in a range between 0.8 and 2.2 eV. The results reveal a pronounced isotopic effect. Plots of the potential energy surface and typical reactive trajectories show the evidence of an additional reaction mechanism for the SD+H product channel. This reaction mechanism, together with mass combination, can explain the isotopic effect for the title reaction.