In order to understand the nano-cutting properties of single crystal germanium and improve the optical surface quality of nano-germanium devices, the three-dimensional molecular dynamics (MD) method was firstly applied to investigate the temperature distribution of the material atoms during the nano-cutting process of single crystal germanium. The anisotropy effect of Ge (100)、(110)、(111) on the cutting temperature and the influence of cutting temperature on cutting force were investigated. It was found that the highest cutting temperature during the cutting process was distributed among the chips, reaching 460K. there is also a high temperature region in the friction zone of the tool back face, the highest temperature is above 400K. Among the three different crystal planes, Ge (111) has the highest cutting temperature, because the atoms between different crystal faces have different spatial structures. Ge (111) has the highest atomic density, namely, Ge(111) is the densely packed surface of the single crystal germanium, which releases the most energy. What’s more, cutting temperature has also played an impact on the cutting force, As the cutting temperature increases, the cutting force of the material atoms will be reduced.