<p>Salt rock creep is a critical factor influencing the stable operation of underground salt rock reservoirs. To investigate the mechanical characteristics of salt rock creep, this study analyzes existing test data to clarify the full damage evolution process during salt rock creep. Mechanical responses to salt rock creep under different stress conditions are explored, and a method for determining the creep initiation stress threshold is proposed based on the characteristics of salt rock’s isochronous stress–strain curves. A new full-stage creep damage model for salt rock is developed by integrating fractional-order calculus theory with damage mechanics and Perzyna’s overstress theory. Methods for calibrating the model parameters using data from uniaxial and triaxial creep tests, as well as isochronous stress–strain curves, are provided. The relationship between the initiation and duration of accelerated creep and stress levels is also established. Extensive model validation results indicate that the salt rock creep model proposed in this study can simulate creep deformation characteristics across all stages, as well as has the capacity to predict the onset and duration of accelerated creep. Furthermore, the model requires only one set of parameters to simulate the creep deformation of salt rock under different stress levels, demonstrating its capability to interpolate and extrapolate creep deformation scenarios beyond the scope of existing test data.</p>