Subsidence of the earth’s surface induced by mining activities has always been a critical concern in the relevant research fields. This subsidence disrupts the original geological structures and can lead to secondary geological hazards, environmental degradation, and threats to human lives and property. An in-depth investigation of this issue led to us using the three-dimensional finite-difference numerical simulation software FLAC3D 6.0 in this study. The research focuses on the Prang Copper Mine subsidence area in Yunnan Province, China, with a particular emphasis on the comprehensive analysis of the formation mechanisms of a large-scale crack appearing on the south side of the subsidence area. The study also includes a predictive analysis of the future development trends of this crack. The simulation results indicate that the crack formation was a consequence of the combined effects of uneven surface subsidence induced by underground structural interfaces and underground mining activities. As mining activities continued, the non-uniform subsidence of the surface intensified. The northward (Y-axis) displacement difference of characteristic points A and B on both sides of the crack continuously increased, signifying the widening of the crack. Mining activities also influence the displacement in the X-axis direction, potentially posing risks to support structures on either side of existing drainage channels. Therefore, effective control measures are warranted. Furthermore, this study highlights the possibility that new mining activities may further exacerbate subsidence on the south side of the subsidence area. This research provides valuable insights into the complexity of surface subsidence and its associated risks, offering guidance for mining activity planning and safety measures.