Columnar jointed rock mass (CJRM) formed by intact rock divided by special symmetrical columnar joints is a special type of rock with poor mechanical properties, strong anisotropy, and weak self-supporting ability, severely affecting the excavation safety and stability of underground tunnels. In this study, taking the Baihetan hydropower station as the engineering background, CJRM geological numerical models with different dip angles that combined well with the natural CJRM were generated based on the geological statistical parameters of the engineering site and were verified to have high rationality and accuracy. Tunnel excavation and overloading tests were carried out on these numerical models, and the results showed that the stress and displacement distributions after excavation exhibited strong anisotropic characteristics under different dip angles, and the positions where engineering safety problems are most likely to occur are the side walls, which are prone to stress-structure-controlled failure mode. The self-supporting ability at different dip angles after excavation from weak to strong are 45°, 60°, 75°, 90°, 30°, 0°, and 15°. The safety factors assessed by overloading for CJRM with dip angles of 0–90° degrees were 2.5, 2.6, 2.6, 1.8, 2.1, and 2.2, respectively, providing a valuable reference for the construction safety and support measures of CJRM excavation.