In this paper, we propose a graphics processing unit-based efficient surgical algorithm for operating on a human liver by a cavitron ultrasonic surgical aspirator (CUSA) scalpel in a virtual environment built with polyhedral objects in Standard Triangulation Language format. First, using z-buffers of a human liver and a CUSA scalpel in a general-purpose graphics processing unit, we rapidly detect their intersections of rectangular parallelepipeds. Then, depending on the plastic, elastic, and viscous material properties of the operated portion of the liver, we determine the rectangular parallelepiped lengths. From that point, based on the correspondence between a vertex and pixel via the XY-image of the z-buffer, the corresponding vertices of the liver polyhedron are moved along the Z-axis of the z-buffer according to its extended or contracted length of rectangular parallelepipeds. By this function, the liver polyhedron can be efficiently and precisely deformed or cut by the CUSA polyhedron.