In this paper we present some of our recent advances in the simulation of surgical procedures including surgical cutting in multimodal virtual environments. Progressive cutting, without the generation of new primitives, is achieved by snapping the nearest nodes to the interaction point between the cutting tool and the underlying polygon edge. The realism of the simulation is enhanced by employing a local subdivision algorithm in the vicinity of the tool-tissue interaction region. A cutting gutter is constructed to display the interior of the cut surface as the cut opens up. A meshfree method is used to compute the deformation fields and interaction forces. Simulation examples involving the cutting of realistic organ models are presented.