Due to the gas injection and production of underground salt caves during the operational phase, rock salt is often subjected to a combined stress of cyclic pressure and constant pressure. In order to investigate the damage evolution of rock salt under different combined stresses, the uniaxial cyclic loading test and cyclic creep test were carried out. The stress-strain curves, energy characteristics, energy dissipation, and damage of rock salt in the two experiments were analyzed and compared. The test results show that the stress-strain curves of the two tests presented three stages of “sparse”-“dense”-“sparse.” As the maximum stress increases, the stage of “dense” will decrease and the rock salt cycle life will decrease. The relationship between cycle life and Δσ (difference between maximum and minimum stress in the tests) is an exponential function under cyclic loading and a linear relationship under cyclic creep. Based on the experimental data, the energy dissipation of rock salt is analyzed. The damage variables were defined from the perspective of energy dissipation, and the damage evolution of rock salt under two tests was obtained. There are three corresponding stages of energy dissipation and damage: initial, constant speed, and acceleration. The damage model is obtained by inverse functioning the s function, and then the correction coefficient is added to the model to obtain the modified damage model. The modified damage model is compared with the experimental data. The results show that the model can accurately describe the three stages of rock salt damage. The significance of parameters in the modifying damage model is also discussed.