To accurately describe the disturbance of underground rock caused by constant-rate loading and simulate the creep physical properties of rock before and after damage, unloading tests to induce damage at 60% of the yield strength under various confining pressures and creep tests with graded loading were conducted. Based on thermodynamic theory, the initial damage variable values under different confining pressures were calculated, revealing the trend of damage variables with varying confining pressures and the changes in strain differences between damaged and undamaged rocks during various creep stages. Combining the theory of component models and damage mechanics, the isochronous creep time (tc) and yield strength (σs) were used to segment the creep stages in modified Maxwell and Kelvin-Voigt bodies. By connecting the Poynting-Thomson body, the modified Maxwell body, and the modified Kelvin-Voigt body in series, a new viscoelastic-plastic creep model was developed.The results indicate that as the confining pressure increases, both the total input energy and unloading energy exhibit an increasing trend. However, for rocks damaged at 60% of peak stress, the damage variable decreases with increasing confining pressure. The study elucidates the tendency for the influence of unloading damage on rock creep stages to increase over time under uniaxial stress conditions and the pattern of this influence first increasing and then decreasing under triaxial stress conditions. The theoretical curves of the new model align with uniaxial and triaxial experimental data with a fit degree of over 0.93, confirming that the constructed viscoelastic-plastic model is applicable to rock creep tests under all stress states and damage levels, and can effectively reflect the mechanical characteristics of the three creep stages. The research findings provide a theoretical foundation for underground rock engineering and offer a new method for constructing creep models.