This paper is devoted to the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Motivated by the fact that the complete information of the semi-Markov kernel (SMK) is difficult to be obtained in practical applications, it is recognized to be partly unknown as the most common mean. By utilizing the prior information of the sojourn-time (ST) upper bound for each switching mode, sufficient conditions under the equivalent DSMC law are proposed for the mean square stability. Moreover, the designed DSMC law realizes the finite-time reachability of the sliding region, and makes the sliding dynamics converge to the pre-designated sliding region in a finite time. In the end, a numerical example and an electronic throttle model are given to validate the proposed control strategy.