In order to study the effect of crystal orientation on the nano-cutting process of single crystal γ-TiAl alloy, molecular dynamic numerical methods were used to analyze and discuss the cutting force, cutting temperature, material removal and lattice structure changes of different cutting crystal directions, revealing different mechanism of crystal orientation on nano-cutting quality of single crystal γ-TiAl alloy. The results show that during the nano-cutting process, the cutting force, cutting temperature, material removal and lattice structure change with the change of crystal surface and crystal direction. When the (010) crystal plane is selected as the cutting plane, the cutting force is smaller, the cutting heat generated is less, the surface processing quality of the γ-TiAl alloy is better, and the lattice structure is changed less. The workpiece in the direction of (010) [100] cutting crystals produces less cutting heat and is the easiest to cut, with the least transformation of lattice structure and the best surface processing quality of the γ-TiAl alloy