Within a mean-field approach, the kinetics of a mixed spin-1/2 and spin-1 Ising ferrimagnetic system with a crystal-field interaction on a square lattice in the presence of a time-dependent oscillating external magnetic field is studied. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variations of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated extensively. The dynamic phase transition points: are obtained and the phase diagrams are presented in the reduced temperature (T) and magnetic field amplitude (h) plane. The global phase diagram of this simple mixed spin includes six distinct topologies and one ordered and one mixed phase. The system also displays one or two tricritical points and a reentrant behavior, depending on the values of the interaction parameters. The phase diagrams are also discussed in the (d, T) plane, where d is the crystal-field interaction and one interesting phase diagram is presented.