In this work, the distribution and evolution of micro-defect in single crystal γ-TiAl alloy during nanometer cutting is studied by means of molecular dynamics simulation. Nanometer cutting is performed along two typical crystal directions: h100i and h101i. A machined surface,  system potential energy, amorphous layer, lattice deformation and the formation mechanism of chip are discussed. The results indicate that the intrinsic stacking fault, dislocation loop and atomic cluster are generated below the machined surface along the cutting crystal directions. In  particular, the Stacking Fault Tetrahedron (SFT) is generated inside the workpiece when the cutting crystal direction is along h100i. However, a “V”-shape dislocation loop is formed in the workpiece along h101i. Furthermore, atomic distribution of the machined surface indicates that the surface quality along h100i is better than that along h101i. In a certain range, the thickness of the amorphous layer increases gradually with the rise of cutting force during nanometric cutting process.