Three-dimensional molecular dynamics simulation of AFM diamond tip nanoscratching on the (100), (110), (111) crystal faces of single-crystal copper were performed to research the effect on the nanocutting process. The evolvements of subsurface defects are analyzed under different orientation and cutting depth. The results show that the regulations of defects evolvement in different orientation are different in nanocutting process. When AFM diamond tip scratches the (111) orientation of single-crystal copper, there exists dislocation which nucleates beneath the tool and propagates downwards along the (1-11) slide plane. With the decreasing cutting depths, the cutting force peak and averaged cutting force decrease; the cutting force of (111) orientation is biggest, and that of (110) orientation is lowest.