The use of renewable energy is an effective means of achieving carbon peaking and carbon neutrality goals. The construction of compressed air energy storage (CAES) plants using salt caverns is an effective way to increase the efficiency of renewable energy use. The stability of the salt cavern envelope is critical to the operation of a CAES plant. Considering the discontinuity and triaxial stress state of the underground salt cavern envelope, a series of triaxial creep-fatigue mechanics tests were conducted on the salt rock using the MTS815 rock mechanics test system. The effects on the creep-fatigue damage of the salt rock were investigated by setting different confining pressures and stress levels. The main research results and conclusions were as follows: (1) The development pattern of triaxial creep-fatigue stress-strain curve was similar to that of ordinary triaxial fatigue, which was also divided into three stages: sparse-dense-sparse; (2) In the creep-fatigue test, the residual strain before the high stress plateau was larger than that after the plateau, which was different from the ordinary fatigue test. This difference decreased with the increase of the confining pressure; (3) The strength and ultimate deformation of the salt rock increased with increasing confining pressure; (4) During the high stress plateau, the massive proliferation of dislocations inside the salt rock crystals and their accumulation at the barriers were responsible for the greater residual strain before the plateau than after it. In this study, the creep-fatigue mechanical properties of salt rocks under different confining pressures were investigated, which could provide a reference for long-term stability studies of CAES salt caverns.