Varying geological conditions and different rock types lead to complex failure modes and instability of interbedded anti-dip rock slopes. To study the characteristics of failure evolution of interbedded anti-dip slopes, a two-dimensional particle flow code (PFC2D) based on the discrete element method (DEM) was utilized to establish an interbedded anti-dip rock slope numerical model for the Fushun West Open-pit Mine based on the true geological conditions and field investigations. The slope model with an irregular surface consists of interbedded mudstone and brown shale as two different rock layers, and a number of small-scale rock joints are randomly distributed in the rock layers. The influence of different inclination angles (20° and 70°) of the rock layer and slope angles (60° and 80°) on the stability of interbedded anti-dip rock slopes was considered. The evolution of the failure progress was monitored by the displacement field and force field. The simulation results showed that the rock joints in the rock stratum promoted crack initiation and increased the crack density but did not change its shear-slip failure mode. A large inclination angle of the rock layers and slope angle can lead to topping slip failure along the slip zone. However, shear-slip instability generally occurs in interbedded anti-dip rock slopes with small inclination angles of the rock layer and small slope angles. These results can contribute to a better understanding of the failure mechanism of interbedded anti-dip rock slopes under different geological conditions and provide a reference for disaster prevention.