Large-scale molecular dynamics simulation is performed to study the nano-cutting process of single crystal copper realized by single-point diamond cutting tool in this paper. The centro-symmetry parameter is adopted to characterize the subsurface deformed layers and the distribution and evolution of the subsurface defect structures. Three-dimensional visualization and measurement technology are used to measure the depth of the subsurface deformed layers. The influence of cutting speed, cutting depth, cutting direction, and crystallographic orientation on the depth of subsurface deformed layers is systematically investigated. The results show that a lot of defect structures are formed in the subsurface of workpiece during nano-cutting process, for instance, stair-rod dislocations, stacking fault tetrahedron, atomic clusters, vacancy defects, point defects. In the process of nano-cutting, the depth of subsurface deformed layers increases with the cutting distance at the beginning, then decreases at stable cutting process, and basically remains unchanged when the cutting distance reaches up to 24 nm. The depth of subsurface deformed layers decreases with the increase in cutting speed between 50 and 300 m/s. The depth of subsurface deformed layer increases with cutting depth, proportionally, and basically remains unchanged when the cutting depth reaches over 6 nm.