A novel approach to simulate soft tissue cutting in a virtual reality endoscopic simulator for surgical training is proposed in this paper. This approach is based on both the improved mass-spring model and the use of computational geometry. A virtual spring is introduced and harnessed to help compensate the shortcoming of the conventional mass-spring model, and a detection algorithm utilizing decomposition of affine coordinates is adopted for the purpose of determining the springs that intersect with the cutting plane. To speed up the simulation performance, algorithms and data structures for the cutting model are designed and implemented based on GPGPU (General-purpose computing on graphics processing units). The performance comparison on the GPU and CPU demonstrates that the proposed method is efficacious and practical.