Variable-frequency air injection and extraction is critical for salt cavern compressed air energy storage (CAES) power plants to smoothly integrate electricity into the power grid, and the magnitude of its effect on the mechanical properties and damage progression of the salt cavern surrounding rock determines the operation scheme of CAES power plants. To examine the impact of variable frequency, a series of monotonic loading tests with different rates and variable-frequency fatigue (VFF) tests with different upper limit stresses were carried out. Dilatancy stresses have a positive power function relationship with loading rate and frequency, but the fatigue loading process weakens this nonlinear tendency. The rate of change (CR) or the exponent of the fitted function can express it. From the initial stage to the steady stage, the CR of dilatancy stress increases about three times, and the CR of residual volumetric strain decreases about five to eight times. Increased upper-limit stress weakens this trend of change. Both high speed and high-frequency loading shift the damage acceleration point forward (e.g., b value accelerates earlier). The damage rate correlation is significant in the later stages of the VFF tests, the rate correlation of damage is significant. Both the upper stress and the extension of the main fracture zone enhance the rate dependence of fracture types. Moreover, the effect of rate on crystal penetrating cracks is more pronounced in the high-stress interval. The number of fractures significantly affects the dilatancy, rather than the type of fracture. This study serves as a guide for the design of variable frequency programs in different CAES salt cavern operation stages, as well as subsequent research.