To ensure the stability of slopes and reduce the risk of slope failure at an open-pit copper-cobalt mine in the DRC, this study conducted an integrated analysis based on engineering geology, field investigations, and laboratory testing. The swelling characteristics of the slope rock mass were identified using typical geological cross-sections, and deformation and failure features were analyked. A numerical simulation method was then employed to evaluate slope stability. The results show that swelling potential can be determined through a combination of visual indicators and test parameters, with different discrimination methods yielding consistent results. Based on moisture content and free swelling rate, the swelling rock strata were classified into an upper weakly swelling layer and a lower non-swelling layer, and corresponding mechanical parameters were established for each. Finite element modeling revealed that zones of equivalent plastic strain matched the distribution of swelling strata, and simulated slope displacements were consistent with observed conditions. On this basis, a slope stabilization scheme tailored for swelling rock in the mining area was proposed. The findings enrich the theoretical framework of special rock and soil mechanics and provide technical support for slope engineering under complex geological conditions.