A differentiable simulator for simulating the cutting of soft materials by a cutting instrument is provided. In accordance with one aspect of the disclosure, a method for simulating a cutting operation includes: receiving a mesh for an object, modifying the mesh to add virtual nodes associated with a predefined cutting plane, optimizing a set of parameters associated with a simulator based on ground-truth data, and running a simulation via the simulator to generate outputs that include trajectories associated with a cutting instrument. Optimizing the set of parameters can include performing inference based on a set of ground-truth trajectories captured using sensors to measure real-world cutting operations. The inference techniques can employ stochastic gradient descent, stochastic gradient Langevin dynamics, or a Bayesian approach. In an embodiment, the simulator can be utilized to generate control signals for a robot based on the simulated trajectories.