The Sanshandao Gold Mine is currently in the deep mining stage. The ground pressure on the surrounding rocks is gradually becoming more considerable, and at the same time, threatened by the overlying seawater, the possibility of mine water inrush accidents is increasing. In this study, the MTS815 rock triaxial seepage test system was employed for the triaxial compression testing and stress–seepage coupled testing of granite under different confining pressures. The results show that granite’s pre-peak mechanical evolution under different confining pressures is divided into four stages (the crack closure stage, linear elasticity stage, stable crack expansion stage, and unstable crack expansion stage). With the increase in the confining pressure, the crack initiation threshold, crack damage threshold, and peak threshold gradually increased, but the closure threshold had no corresponding change. Moreover, in the loading process, the permeability curve first decreased and then increased, and the confining pressure suppressed the peak permeability of granite. Finally, based on the test results, stress sensitivity analysis was carried out, and it was found that polynomials fit the relationship between permeability and effective stress better. Granite’s permeability showed strong stress sensitivity at medium confining pressures. The stress sensitivity of the permeability of granite decreased with increasing effective stress at medium and high confining pressures, while it tended to increase at low confining pressures.