Despite the digital era and the emergence of simplified production paradigms enabled by digital twin technology, traditional manufacturing processes like lathe machining are invaluable because of their ability to meet various and multiple needs reliably and flexibly. To combine these processes into smart monitoring and controlling systems, including tool wear detection and fault diagnosis, precise multi-axis force measurement is necessary. Single-axis sensors are insufficient to measure the entire dynamics of cutting interactions. A new idea based on strain gauge technology of a self-decoupled three-axis force sensor is proposed in this paper, which is to measure cutting forces and vibration in a lathe operation. During the process of cutting, the sensor is designed to recognize independently the onset of forces at three orthogonal axes to enhance real-time process monitoring capabilities. The Timoshenko beam theory is used to design the mechanical structure, where sensitivity could be improved, and with minimal crosstalk. Finite Element Analysis (FEA) simulations were conducted to evaluate the sensor’s performance, the stress distribution, the modal assessments, and the interference error. The interference error of 0.31 percent indicated by the results of the simulation is extremely low, indicating a successful decoupling of the force components. These encouraging simulation results indicate that there is a high possibility of applying the proposed sensor design to intelligent manufacturing systems. It presents an initial point of departure into the embodiment of sophisticated monitoring platforms for conventional machining processes, eliminating the discontinuity between old and new smart manufacturing systems.