In this paper, we propose algorithms to generate realistic cut simulations on hybrid deformable anatomy objects consisting of volumetric data and iso-surfaces. A 3-dimensional node snapping algorithm is presented to modify the surface topology of the objects, without adding new elements. Smooth cut is generated by duplicating and displacing mass points that have been snapped along the cutting path. A volumetric deformable model is employed underneath the surface, with the internal structure and material properties of the heterogeneous objects revealed along the opening. A 3D Chainmail deformation algorithm is used for the deformation of the volumetric model to enhance the realism. A haptic device is integrated into the simulation system as a cutting tool to trigger the progressive cutting procedure, and to feel the different volumetric components. The simulator incorporates the simulation of surgical prodding, pulling and cutting. Advanced features include the separation on the cut surfaces and post-cutting deformations like wrinkle effect. The proposed cutting techniques can be used in surgical simulation or other virtual simulations involving topological modification of heterogeneous soft materials to enhance the fidelity and realism