In this paper, the repetitive nano-cutting process of single crystal γ-TiAl alloy was simulated by molecular dynamics method. The evolution of cutting force and microstructure defects in the repetitive nano-cutting process was studied. The roughness and residual stress of the machined surface were analyzed, and the difference between repetitive nano-cutting and single-cutting was discussed. The results show that the repeated nano-cutting process is accompanied by the formation and annihilation of dislocations, and the fluctuation of dislocation line length in the second cutting process is less than that in the first cutting process, and the cutting state is more stable; The cutting force increases rapidly in the initial stage of machining, and then the cutting force enters the stable machining stage. At the same time, it is found that the cutting force of the second cutting is less than that of the first cutting. After secondary cutting, the residual stress distribution is more uniform and the residual compressive stress of the machined surface layer increases due to the secondary extrusion of the tool; Secondary machining can improve surface quality and reduce subsurface damage, while the increase of residual compressive stress and the increase of energy required for machining reduce the plasticity of the machined surface, so that the tertiary machining has no obvious improvement on both.