Dynamic magnetic hysteresis properties in a two-dimensional mixed Ising system designed with integer and half-integer spins, namely spin-1 and spin-5/2, are investigated comprehensively on the basis of the mean-field approximation and the Glauber-type stochastic dynamics, namely dynamic mean-field approximation (DMFA). In particular, we examine the effect of Hamiltonian parameters on dynamic hysteresis properties. As a result of this examination, some characteristic hysteresis behaviors are obtained, such as the existence of single, double and triple hysteresis. Moreover, we study to obtain coercive field and remanent magnetization. Our results are compared with some experimental and theoretical works to find a qualitatively good agreement.