The cutting process finite element simulation technology is a numerical method to simulate the cutting process， which can investigate various physical mechanisms caused by material removal during the cutting process. It has significant advantages in optimizing cutting parameters， improving machining quality， and reducing research costs. The significantly investigate objective is how to make the finite element simulation of cutting process more consistent with actual cutting process， so numerous research on finite element simulation technology for cutting has been carried out both domestically and internationally， and the relevant achievements have been applied in engineering. This paper provides an overview of the basic principles， advantages， and development trends of geometric simulation and physical simulation in cutting process finite element simulation. It systematically summarizes the development of constitutive models and mesh partitioning by domestic and foreign scholars to improve the accuracy and efficiency of cutting machining finite element simulation. On this foundation， the research progress of the combination of geometric and physical simulation methods is summarized. Finally， the important issues and future development trends of finite element simulation technology for cutting machining are envisioned.