Abstract: With the development of the mining industry, a large number of accessible shallow mineral resources are being depleted, and some have now been completely exhausted. The exploitation of the Earth’s deep mineral resources has become the only way to meet the society’s growing demand for minerals. With the increase in mining depth, the geostress, temperature, and pore pressure of water increase significantly, and the nonlinear mechanical behavior of rock becomes prominent. To assess the damage and failure of surrounding rock in deep shaft under high osmotic pressure and asymmetric geostress, a coupled mechanical–hydraulic–damage model was proposed to examine the effective stress of surrounding rock in deep shaft. This approach took into account the maximum tensile stress criterion with shear failure based on the Mohr–Coulomb criterion and was applied to simulate damage evolution in heterogeneous rocks. On this basis, the mechanisms of pore pressure, rock permeability, and geostress and its effects on rock damage evolution and fracture propagation were further investigated. The results indicate that the larger the pore pressure and its gradient are, the larger the damage and failure areas of surrounding rock. With the decrease of permeability of country rock, the damage and failure areas of country rock gradually increase and tend to be stable. The geostress field plays an important role in controlling the failure morphology of surrounding rock. When the ratio between maximum and minimum horizontal principal stresses is small, the damage and failure zones of the surrounding rock are concentrated in the direction of the minimum horizontal principal stress, mainly shear damage. However, if the ratio is large enough, then the tensile damage zone may occur in the direction of the maximum horizontal principal stress. Notably, the ratio of the maximum horizontal principal effective stress to the minimum horizontal principal effective stress increases because of the presence of pore pressure. Therefore, a high pore pressure in the formation could increase the risk of tensile failure of surrounding rocks. The findings of this research can be applied to the optimization of the shaft design to avoid areas with high tectonic stress and high pore pressure and ensure the safety of shaft construction.