Dynamic disturbance is an important factor for the failure of surrounding rocks in underground engineering projects, particularly under high static stress conditions. In this study, three dynamic disturbances are considered: a single-pulse dynamic load with a large stress amplitude (a mild disturbance), a low-frequency cyclic dynamic load with a moderate stress amplitude (a modest disturbance), and a high-frequency cyclic dynamic load with a small stress amplitude (a weak disturbance). Based on the true-triaxial experiments of coupled static and dynamic loads, the mechanical behaviors and acoustic emission characteristics of the dynamically induced rock failure are analyzed. The test results show that the dynamically induced rock failure depends not only on the initial static stress level but also on the dynamic disturbance type. In the rock failure induced by the mild disturbance, the increasing initial static stress produces the dual effect of an initial increase and then a decrease in the failure strength of the rock specimens. In the rock failure induced by the modest disturbance, a sufficiently high initial static stress is the basic condition to trigger rock failure. In the rock failure induced by the weak disturbance, the initial static stress threshold value needed to trigger the rock failure is higher than that needed for the modest disturbance. The rock failure induced by the mild disturbance is mainly contributed by the large input of disturbance energy and the slight impact effect. The rock failure induced by the modest disturbance is mainly contributed by the fatigue damage effect, which reduces the ultimate energy storage capacity of the rocks. The rock failure induced by the weak disturbance is related to not only the fatigue damage effect intensifying the specimen damage, but also the dynamic disturbance effect inducing the release of elastic strain energy. Additionally, the fracture mode for rocks subjected to the mild disturbance is predominantly the shear fracture mode. More tensile cracks are detected for rocks subjected to the modest disturbance than those subjected to the mild disturbance. More shear cracks and fewer tensile cracks are detected for rocks subjected to the weak disturbance than those subjected to the modest disturbance.