In recent years, the movement of machine tools including 5-axis control machining centers (5 MC) and turning centers has progressed to enable machining at high speeds and high degrees of accuracy. The accuracy of simultaneous three-axis movement at very high feed speeds has increased significantly. Specifically, with the development of control technologies for these machine tools featuring simultaneous three-axis control, the accuracy of helical interpolation motion at high feed speed has achieved a sufficient level to perform processes such as screw cutting with a thread mill tool. Boring machining and pocket machining for difficult-to-cut materials are processing methods that employ helical interpolation movements with an endmill tool, and it is becoming a promising technology in light of recent advancements. Therefore, we looked at screw cutting with a thread mill tool and proposed a novel monitoring method to improve the accuracy of machining the screw by deriving the radial force of thread cutting from three components — two forces in the X and Y directions and torque around the Z axis — using a piezoelectric dynamometer. In this study, we also investigated the accuracy of machining the screw when the pilot hole and screw were drilled at the same time as well as the accuracy when the pilot hole is drilled beforehand. In addition, we monitored the cutting data and X-Y feed motions using a wireless holder and CNC information to construct a smart manufacturing method for machining screws using helical interpolation. As a result, the proposed monitoring method is effective at improving the accuracy of machining screws from various work materials using helical interpolation motion of a thread mill tool.