During underground hard-rock mining, the drilling and blasting method currently remains the most economical excavation method, and the rock may experience a multistrain-rate spectrum under quasi-static, dynamic, and rheological loading conditions and their combination as well. The study on the damage mechanism of rock under multistrain-rate condition that induced by mining excavation is the fundamental issue for predicting the mining-induced hazards such as rockburst. In this study, the state of the art of rock damage and failure under different strain rates is reviewed first. Then, the numerical model for rock failure under multiple strain rates is formulated when the rock damage is taken as the main thread. Meanwhile, we summarize our work in this area over the past ten years, and the constitutive law for the damage and failure of rock under multistrain rates is presented. Finally, several numerical examples, i.e., rock damage and failure under combined static and dynamic load, rock damage and failure triggered by dynamic stress redistribution due to excavation, rock damage and failure induced by blasting, and rock damage and failure due to the combination of dynamic disturbance and rheological load, are presented. Based on these numerical simulations, the associated rock damage mechanism and failure behaviors under differently combined multiple strain rates are clarified, which may provide a theoretical basis for clarifying the rock failure mechanism during rockbursts and rock blasting. Also, further studies on the damage and failure of rock under multiple strain rates are suggested.