Quantum time-dependent wave packet dynamics studies on the nonadiabatic Be+(P-2) + HD -> BeH+/BeD+ + D/H reaction are performed for the first time employing recently constructed diabatic potential energy surfaces. Strong intramolecular isotope effects and unusual results are presented, which are attributed to the dynamic effects of shallow wells induced by avoided crossing on the diagonal V-22(d) surface. The BeH+ + D and BeD+ + H channels are dominated by high-I and low-J partial waves, respectively. The BeD+/BeH+ branching ratio is larger than 10 at low energy and gradually decreases with increasing collision energy. The BeH+ product is primarily distributed at low vibrational states, whereas there exists an obvious population inversion of vibrational states on the BeD+ product. The results of differential cross sections suggest that the formation of the BeH+ + D channel favors a direct reaction process, while the BeD+ + H channel is mainly generated by the complex-forming mechanism.