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Composite structure with amorphous layer and crystalline substrate is important for nano-machining. In order to study the influence of amorphous layer structure on the nano-cutting mechanism and mechanical properties of single crystal germanium (Ge), molecular dynamics (MD) simulations were carried out on the nano-cutting process of amorphous-crystalline layered structure (A-C model) with different amorphous layer thicknesses. Cutting force fluctuation, stress status, subsurface damage characteristics and material removal, which are the key issues in nano-machining were analyzed. The result shows that as the thickness of amorphous germanium (A-Ge) increases, the cutting force and stress decrease, and the cutting temperature increases. The plasticity of the material is enhanced as the thickness of A-Ge increases, which is due to the softening of A-Ge when the cutting temperature rises. When the thickness of A-Ge is the same as the cutting depth, the material has lower subsurface damage and higher material removal rate, so it has excellent mechanical properties.