The dynamics of the dissociative charge exchange reaction He++H-2(upsilon less than or equal to 4)-->He+H+H+ is investigated theoretically at a relative collision energy ranging from 2 eV to 10 eV. Because of the weakness of the nonadiabatic couplings involved in this process, it has been possible to use a new method, which consists in dividing the theoretical treatment in two parts; a semiclassical coupled wave packet method describes the charge exchange between He+ and H-2, while the dynamics of the dissociation of H-2(+) in the presence of the He atom is handled classically. The time dependent description of the reaction provides a simple interpretation of the strong dependence of the cross section with the collision energy and the initial vibrational excitation of H-2. It is shown that the reaction mechanism is qualitatively different for the different initial vibrational quantum states of H-2. An interesting dynamical effect is observed in the upsilon = 0 case; the H+ ions are scattered primarily in the forward direction relative to the initial Hz direction, while the neutral H atoms are backward scattered. Moreover, the H+ ions are on average faster than the neutral H atoms. The results are successfully compared with the available integral and differential experimental data.