Catastrophic failure of rock mass is a kind of serious geological hazard which usually happens during deep mining excavation and underground engineering construction. Though many investigations have confirmed that it was strongly relate to dynamic disturbances, the disturbing mechanism is still not well-known. The purpose of this paper is to offer a theoretical method to analyze dynamic disturbances induced catastrophic failure. On the basis of synergetic analysis, we established a generalized Langevin equation to describe the nonlinear evolution process of rock mass by considering stochastic dynamic disturbances. Then we further derived a stochastic potential function to research the inductive effect of dynamic disturbances and critical property of catastrophic failure. Results indicate that the influence of dynamic disturbances on the stability of rock mass depends on both the static state of rock mass and the external disturbance intensity. The catastrophic failure threshold is the function of disturbance intensity and control parameters of rock mass.