In this paper, we use an enhanced surface mesh model to simulate virtual dissection by progressive subdivision and re-meshing. Enhanced novel algorithms to generate interior structures that show the result of a cut that is generated by the interaction between instrument and model is used as the underlining framework. The notion of a cross cutting is introduced and solved to offer a more realistic interactive environment for various virtual diagnostic and dissection tasks. Our simulator supports two types of cutting: "cut-into", an instrument penetrating simulated tissues, and "cut through", an instrument cutting through tissues. In either case, a groove is developed in the path where the cutting has taken place to reflect the depth of the cut. Generation of a groove introduces a challenging problem when two cuts cross in their paths. For example, when two cutting path intersects (i.e., an occurrence of cross cutting), the current structures involved in the proximity of the cuts do not simulate a realistic intersecting cross cut. Although many studies have represented solutions to surface mesh cutting, a solution to an interactive cross cutting has not been adequately addressed yet. This paper presents an algorithm that can be flexibly applied for the simulation of an interactive cross cutting on a surface-mesh. Such solution can be further applied to many applications involving surface mesh.