The residual stress of parts is one of the critical factors affecting the machining quality during the cutting process. Visualizing the evolution process of residual stress field in virtual environment can effectively monitor its evolution law, which helps to improve the machining quality of parts. In order to achieve real-time mapping of stress field in virtual environment, a real-time mapping method for stress field in clamping was developed based on digital twin technology. Firstly, the overall architecture of the digital twin in the cutting process was elucidated. Secondly, a mapping scheme for the residual stress field during the machining process in a virtual environment was proposed. Specifically, based on the finite element simulation method, an approximate model for the simulation of residual stress during clamping was established using RBF neural networks; The data-driven method was used to achieve the mapping of approximate model simulation results in a virtual environment. Finally, taking the distribution of residual stress field during workpiece clamping as an example for verification, the maximum deviation between the real-time simulation results of the approximate model and the finite element simulation results is 7.7%, which verifies the feasibility and effectiveness of the real-time mapping method for stress field. In general, this method provided the technical support for digital twin in the cutting process.