Time-dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations have been carried out for the reaction S(P-3) + HD(X-1 Sigma(+)(g)) at the lowest 1(3)A" state with both rotational and vibrational excitations of reactant HD. The calculated integral cross sections from QCT agree fairly well with the TDWP calculations. The reaction probability results from TDWP show that the reaction displays a strong tendency to the SD channel. When the reactant HD is vibrationally excited, both channels are promoted apparently. The vibration of the HD bond tends to reduce the difference of reactivity between the two channels. The detailed state-to-state differential cross sections (DCSs) are calculated. These distributions show some significant characters of the barrier-type reactions. At the same time, the scattering width of product SD has a certain relationship with its rotation excitation. For the vector properties, P(theta(r)), P(phi(r)), and P(theta(r),phi(r)) distributions are calculated by QCT, and the increased collision energy weakens the rotational polarization of the SD molecule.