Modeling cuts, bleeding and the insertion of surgical instruments are essential in surgical simulation. Both visual and haptic cues are important. Current methods to simulate cuts change the topology of the model, invalidating pre‐processing schemes or increasing the model's complexity. Bleeding is frequently modeled by particle systems or computational fluid dynamics. Both can be computationally expensive. Surgical instrument insertion, such as intubation, can require complex haptic models. In this paper, we describe methods for simulating surgical incisions that do not require such computational complexity, yet preserve the visual and tactile appearance necessary for realistic simulation.