Abstract: The laser cutting machine feed drive system is a servo motor-driven system, where its transmission components generate vibrations during high-speed and high-acceleration feeding processes due to external excitation or self-induced oscillations of the system. These vibrations adversely affect the positioning accuracy and surface processing quality of the CNC equipment, decrease the operational efficiency and lifespan of CNC equipment, and may even result in damage to the CNC system. In this paper, the transformation Lie group is introduced to study the Noether symmetry theory of torsional vibration problem using the HLH 2040 laser cutting machine manufactured by Jiangsu Yawei Machine Tool Co., China as an example. In addition, the motion law and state response characteristics of the problem are given. The Lagrange equation of the system is established by finding the kinetic and potential energies of torsional vibration of the servo-driven ball screw feed transmission system and constructing the Lagrange function. By introducing infinitesimal transformations about time and generalized coordinates, Noether’s theorem of torsional vibration of the system is proposed and proved. The conserved quantities of the system are found to exist, and symmetry relations exist in the obtained conserved quantities. The principle behind movements is given according to the conserved quantities existing in the torsional vibration of the system. The dynamic response characteristics of the system are analyzed, and the dynamic response is numerically simulated. In conclusion, results prove that, after the system is supplied with specific technical parameters and the effect is remarkable, along with using the symmetry method in this study, the system can able to stabilize rapidly in about 10ms. This study effectively reduces and manages the torsional vibration issue in the servo motor-driven feeding process, which holds significant importance in enhancing the machining quality and efficiency of CNC equipment, as well as extending the operational lifespan of CNC systems.