During underground mining excavation, dynamic disturbances (e.g., blasting) may accelerate rock creeping and induce unstable failure. It is crucial to properly quantify the impact of dynamic disturbances on creeping behavior to understand the long-term effects of underground excavation on rock media. A damage-based creep model was established in this study and implemented in Fast Lagrangian Analysis of Continua in 3D (FLAC^3D) to quantify the damage and unstable failure of creeping rock triggered by dynamic disturbance. This model reveals the mechanical behavior of rock under creep-impact loading. It was verified by calculating the viscoelastic deformation around circular excavation, by reproducing the damage process under static loading, and by simulating the rock damage and failure under creep-impact loading. The model was then used to examine the mining-induced creep deformation around an operational shaft in Xincheng Gold Mine, China, where both the mining-induced creep of the country rock mass and dynamic disturbance of blast-induced vibration were considered. Numerical simulation indicated that the dynamic disturbance could accelerate the damage of rock under creep stress, which may be an important factor to trigger the accelerating creep of rock, even though the unstable failure of rock lagged behind the dynamic disturbance. The case study on the shaft stability analysis indicated that the dynamic disturbance could accelerate the time-dependent deformation of the shaft, the first dynamic disturbance induced much more shaft deformation, while in long-term creep (e.g., 5 years), the effect of blasting vibration was not significant. The trend and magnitude of shaft deformation agreed with the in situ measurements, which indicates that the numerical simulation could be used to predict the long-term shaft deformation in future.