Water inrush is one of the most serious threats to the construction safety of karst tunnels. Numerical simulation is one of the important means of underground engineering research, which is of great significance for revealing the evolution process of water inrush. In this study, an improved peridynamic model is established to simulate the formation process of water inrush channels due to rock mass progressive failure in karst tunnels. The results show that the surrounding rock between the karst cave and the tunnel excavation area is gradually damaged under the integrative action of excavation disturbance and karst cave water pressure during tunnel excavation. The initiation, propagation, and coalescence of cracks in the surrounding rock are spontaneous, and the water inrush channels are finally formed by the cracks. Based on the improved peridynamics, a total of 21 simulations were performed to study the influence law of different factors on the evolution process of water inrush channels. The influencing factors mainly include water pressure and radius of karst cave, distance between karst cave and tunnel, elastic modulus, and tensile strength of rock mass. Through the analysis of the morphological difference of water inrush channels and the damage degree of the surrounding rock under different calculation conditions, the formation mechanism and evolution process of water inrush channels are revealed. The research methods and results can provide some guidance for disaster prevention and mitigation of karst tunnel water inrush.