A fault disrupts the continuity of the rock strata in a mining area. To study the law governing the fracture of overlying strata in mining areas under discontinuous boundary conditions, the overlying strata were redefined and grouped based on the activity characteristics of each rock layer during the overall movement of the overlying strata. The activity patterns of different layers of the fault were obtained through the movement and failure forms of each group of rock layers. The relationship among the size of the coal pillar at the boundary of the fault, the dip angle of the fault, and the movement angle of the rock strata was considered. A model of the spatial relationship between the overlying rock movement zone of the quarry and the fault surface was established. The limit equilibrium equations of the key layer in the fault zone before breaking were established based on the tensile strength of the rock layer. In addition, the mechanical slip instability criterion and the deflection instability criterion of the discontinuous-boundary rock mass are given herein. Based on a field case, a double criterion was used to determine the initiating activated rock layers of the fault in the cases where the fault dip was smaller than the rock movement angle. Rock movement during excavation was simulated by similar simulation tests, and different levels of rock movement patterns in the boundary fault zone were focused on monitoring and analyzing. The stress and displacement changes in different rock layers in the fault zone were analyzed with numerical simulation results. The results show the following: if the dip angle of the fault is smaller than the movement angle of the rock layer, the delamination space of the fault surface is mainly distributed in the bending and sinking zone of the overlying rock; with an increase in the working-face advancement distance, the vertical pressure of the upper part of the fault gradually decreases, and the stress-concentration area in the middle and lower part of the fault gradually increases; the rock layer of the upper part of the fault, which is mainly composed of the key stratum, is the main area of activation of the fault.