We propose a variable threshold based cutting method for tetrahedralized deformable objects used in virtual surgery simulations. Our method uses cut-nodes and cut-edges scheme to determine cutting path with variable threshold improvement. Static threshold may cause ambiguity in cut-node selection when the threshold is so large that one of two vertices of the triangle to be cut can be selected as a cut-node. In addition, small threshold value results in many tetrahedrons while a smooth cut and large threshold value leads to a more jagged incision with less small tetrahedrons. Thus, both small and large threshold values have advantages and disadvantages. Simulation results show that our variable threshold based cutting method offers relatively better results than static threshold based one in terms of advantages and disadvantages mentioned above.