Abstract: A method and apparatus has been developed for metal cutting machine using a cutting die tool that pivots as it cuts a metal workpiece. By pivoting the cutting tool, the orientation of the metal surface being cut in the workpiece may be varied along the cutting path. A particular application of the invention is for screw metal cutting machine, e.g., a Swiss-type screw lathe, that cuts screw threads in screw blank rods, such that the threads have a variable cant along the length of the screw. The cutting die tool is mounted in a tool holder that is pivoted by a computer controller in accordance with machining instructions for the screw or other device being machined.