Based on experimental investigations, we propose a coupled elastoplastic damage model to simulate the mechanical behavior of granite under compressive stress conditions. The granite is taken from the Beishan area, a preferable region for China’s high-level radioactive waste repository. Using a 3D acoustic emission monitoring system in mechanical tests, we focus on the cracking process and its influence on the macroscopic mechanical behavior of the granite samples. It is verified that the crack propagation coupled with fractional sliding along the cracks is the principal mechanism controlling the failure process and nonlinear mechanical behavior of granite under compressive stress conditions. Based on this understanding, the coupled elastoplastic damage model is formulated in the framework of the thermodynamics theory. In the model, the coupling between damage and plastic deformation is simulated by introducing the independent damage variable in the plastic yield surface. As a preliminary validation of the model, a series of numerical simulations are performed for compressive tests conducted under different confining pressures. Comparisons between the numerical and simulated results show that the proposed model can reproduce the main features of the mechanical behavior of Beishan granite, particularly the damage evolution under compressive stress conditions.