Simulating cutting processes of human tissue is an important feature in virtual reality systems for medical training and rehearsal. In this paper we present a method to simulate the cutting operation in voxel-based virtual reality objects intended to simulate volume cutting in transurethral resection of the prostate. The method allows the user to directly interact with the three dimensional model in a manner that simulates dragging a resectoscope loop through the tissue, performing the task in an intuitive, natural manner.