Simulation of cutting is essential for many applications such as virtual surgical training. Most existing methods use the same triangle mesh for both visualization and collision handling, although the requirements for them in the interactive simulation are different. We introduce visual-collision binding between high-resolution visual meshes and low-resolution collision meshes, and thus extend the spatially reduced framework to support cutting. There are two phases in our framework: pre-processing and simulation. In the pre-processing phase, the fvisual-collision binding is built based on the computation of geodesic paths. In the simulation phase, the cutting paths are detected on the collision triangles and then mapped to local 2D coordinates systems in which the intersections between visual mesh and the cutting paths are calculated. Both collision and visual meshes are then re-meshed locally. The visual-collision binding is updated after cutting, based on which the collision-simulation and visual-simulation embedding are updated locally. Experimental results show that our cutting method is an efficient and flexible tool for interactive cutting simulation.