The dynamics of a domain wall driven by a spin-polarized current in a mesoscopic system is studied numerically. Spin mixing in the states of the conduction electrons is fully taken into account. When the Fermi energy of the electrons is larger than the exchange energy (E(F) > J(sd)), the spin precession induces spin-wave excitations in the local spins which contribute towards the displacement of the domain wall. The resulting average velocity is found to be much smaller than the one obtained in the adiabatic limit. For E(F) < J(sd), the results are consistent with the adiabatic approximation except for the region below the critical current where a residual domain wall velocity is found.