Dam breaches can result in catastrophic flooding, leading to severe economic and property losses downstream. Accurately simulating the dam breaches requires modeling both erosion and slope instability. However, traditional mesh-based methods cannot directly capture the large deformations of destabilized slope soil. A numerical model based on the meshless method Smoothed Particle Hydrodynamics (SPH) is used to simulate dam breaches. It employs an erosion rate-based erosion model to simulate the gradual erosion process and utilizes the Drucker-Prager elastic-plastic model to capture the large deformation of the side slope soil. This model is validated through three benchmark cases: column collapse, bottom flushing by a dam-break flow, and dam breach. Meanwhile, the dam breach processes are analyzed. Results show that the dam breach unfolds in two stages: headward erosion and overall erosion. The onset of overall erosion coincides with the occurrence of slope instability. The influences of the internal friction angle ϕ and cohesion c on the dam breaches are investigated. With increasing ϕ and c, there is less instability and deformation occurring on the side slopes, thus delaying the lateral expansion of the breach. Compared to traditional mesh-based methods, the SPH framework enables direct simulation of large deformations of the side slope. This advantage contributes to further research on dam breach phenomena, such as simulating the interaction between the structure and the soil during the breaching.