Timely prediction of a landslide dam breach is particularly important for assessments of expected disaster consequences and to plan emergency responses. However, due to the complex composition and specific geotechnical properties of the landslide dam material, such a prediction is challenging. In this study, geological survey results and landslide dam breach mechanisms were used to develop a numerical model for overtopping-induced landslide dam breaches, considering variation of soil erodibility with depth. The model included a hydrodynamic process module, a soil erosion module, and a breach evolution module. Moreover, a time step iteration algorithm was adopted to simulate the soil and water coupling process during dam breach. A comparison of calculated and measured breach hydrographs, variations of dammed lake water level, breach sizes, as well as two other typical models were used to validate the rationality of the numerical model, by considering the Baige landslide breach case of November 3, 2018 with detailed measured data. Parameter sensitivity analysis showed that the soil erodibility coefficient exerted an important influence on the breach process, while soil critical shear stress had a relatively small influence (which remained within ±15% for output parameters when it was multiplied by 0.5, 1.0, and 2.0). Furthermore, spillway excavation was found to significantly reduce the peak breach flow if the dammed lake has a large storage capacity, thus identifying it as an effective measure for disaster mitigation.