Landslides are a commonly encountered natural disaster throughout the worldwide. Among the various contributing factors, water is one of the major factors to induce slope instability. This work investigates the landslide problem induced by the combined action of rainfall infiltration and groundwater. To explore the correlation characteristics between the stress and stability of the dump slope under the coupling action of groundwater and rainfall, a mechanical model of the dump slope under the coupling action of groundwater and rainfall was established and a theoretical solution of FoS was developed to accommodate the effects of the seepage action of water and the strength reduction of soil in the process of water migration. It was determined that the primary factor inducing slope instability can change with groundwater and rainfall conditions. There exists a critical wetting front and critical groundwater depth where the dominant factor affecting slope safety changes, and a method for calculating the critical depth for slope instability is proposed. As groundwater depth increases, the critical wetting front depth increases; correspondingly, the critical FoS decreases. As the depth of the wetting front extends, the critical groundwater depth rises and FoS decreases. Meanwhile, the theoretical solutions are validated in a case study for the Shengli #1 open-pit mine. The results of the study may provide directional guidance for the stability analysis of similar slopes.