Quantum time-dependent wave-packet calculations have been carried out to explore the state-to-state dynamics of the ion-molecule (H-(D-),HD) collisions on two accurate ab initio potential energy surfaces in the collision energy range 0.2-1.2 eV. Total and final state-resolved integral and differential cross sections are elaborated in detail. The differential cross sections vary substantially with the collision energy, turning from predominantly backward-scattering at low collision energies to forward and sideways scattering bias at relatively high collision energies. The rebound, stripping and time-delayed mechanisms are found to be possible in (H-(D-),HD) collisions. A set of quasi-classical trajectory calculations were performed, and the results indicate that the backward-scattering peak is caused by the low impact parameter trajectories, while the trajectories of high impact parameter are responsible for the forward scattering. A set of representative state-to-state differential cross sections at collision energies 0.6 and 1.2 eV are also presented. Different reaction mechanisms are dominant in (H-(D-),HD) collisions at different collision energies, resulting in different product rovibrational state distributions. The differences between the dynamics results based on the two potential energy surfaces are also discussed.