A thread cutting attachment for use with conventional type engine lathes for the purpose of semiautomatically cutting threads externally on a workpiece, or with a modified embodiment, internally of a workpiece. Each attachment has structure for securely affixing same to the conventional cutting tool holder of such a lathe. A main body of the attachment has a movable cutting tool holder therewithin. The cutting tool holder is suitably actuated through mechanical means from the energization of a fluid cylinder having a piston with rod extending therefrom. Suitable fluid control structure is connected to this fluid cylinder for actuation thereof under the control of either electrical, pneumatic, or hydraulic control apparatus. The present invention cuts threads like the old conventional thread cutting method, except in the method of the present invention, the single point thread cutting tool automatically disengages after the thread cutting stroke, and the cutting tool automatically engages at the beginning of the thread cutting stroke. The present invention eliminates the need for quickly disengaging the cutting tool manually at the end of the thread cutting stroke. The present invention does not need an undercut in the workpiece, thus allowing the cutting tool to cut dead end threads internally or externally.