Considering the wide distribution range of deposits, the complicated geological conditions, and the potential detriment to slope stability during the caving period, underground goaf and slope stability is a critical concern in the Yangla copper mine. In this paper, goaf and slope stability is studied by implementing empirical analysis and numerical simulations with an equivalent continuum model. An overall understanding of underground goaf stability is obtained by the Laubscher graph method, and an approach composed of the geological modeling technology GoCAD and the specialized meshing tool Griddle is proposed to manage the geological database and prepare the numerical model for stability analysis with FLAC 3D . The Hoek–Brown constitutive model is introduced to simulate the complicated mechanical behavior of rock mass in the process of mining, i.e., the brittleness and confinement effect of rock mass. The key orebodies KT2 and KT5 develop in reverse inclination from slope surface to the inner slope with a maximum depth of 900 m, which means the rock mass bears a high stress induced by mining. The mechanical parameters are calibrated carefully by performing mining simulations that are consistent with the field instability phenomenon and measurement results. In particular, rock-mass behavior is predicted by sensitivity modeling in consideration of the goaf span, mining sequence, and material filling, the aim of which is to optimize the mining design to maintain slope stability during the third mining phase. The calculation results indicate that large deformations at the roof of the goaf and pillar are a critical problem in the Yangla copper mine as they are detrimental to slope stability. Moreover, many goafs collapse during the second and third phases of underground mining, which is also detrimental to slope stability, and the span of the goaf with a deep buried depth needs to be adjusted from 36 to 24 m in the third mining phase. The slope is stable in the second mining phase, but, in the third phase, it enters the large-scale instability state due to the destruction of the rock-mass structure near the slope surface by underground caving. Accordingly, goafs with the potential for collapse should be filled with high-strength materials to maintain slope stability.