A process and system for performing orthopaedic surgery with the use of computer systems and robotic assistance to remove bone, bone cement, and a bone prosthesis, typically a bone prosthesis used in hip replacement surgery, knee replacement surgery, and the like. The process for replacing one or more bone prostheses using a robotic system includes receiving image data comprising an image of each bone, including at least one prosthesis implanted within each bone; creating three-dimensional models of the prosthesis, and the bone; creating a plan for positioning new prostheses within the bone; determining the location and amount of bone and any non-bone material to be removed for the new prostheses; and removing the bone prosthesis from the bone. The inventive process may be used for the replacement of hip joints, shoulder joints, ankle joints, wrist joints, finger joints, toe joints, or other joints.