The construction of large-scale infrastructure projects has formed a large number of soil-rock mixed slopes, and the project cannot avoid the seismic zone. The stability of the soil-rock mixed slopes by earthquakes has become a difficult problem in the engineering community. This paper takes the soil-rock mixture slope in the southwest region as the research object. Based on the field geological survey, data collection, and data analysis, the finite difference method is applied. The stability of the soil-rock mixture slope under the action of numerical simulation (FLAC-3D elastoplastic theory) is carried out, and the stability and damage degree of the soil-rock mixture slope under the action of different propagation directions of seismic waves under the conditions of large, moderate and small earthquakes are analyzed. Studies have shown that under the condition of small earthquakes, the slope is in a stable state. Under the conditions of moderate and large earthquakes, the seismic waves parallel to the empty surface and the vertical seismic waves cause only partial slopes to slide. However, the seismic wave perpendicular to the empty surface caused a landslide on the slope as a whole. It is concluded that the seismic waves perpendicular to the empty surface, propagating in three directions, parallel to the empty surface, and vertical to the empty surface have successively weakened influences on the stability of the slope. The research results can be applied to engineering practice, provide guidance for design and construction, and help improve the stability and reliability of the project.