Molecular dynamics analysis is employed to reveal the atomic-scale details of the material removal process. This method is important to study the nanoscale machining mechanism of nanometric cutting. This article investigates the effects of the polishing speed and a water environment on the polishing force, stress distribution, subsurface deformation, and damage distribution during the nanometric mechanical polishing of the lutetium oxide single crystal using molecular dynamics simulations. The amorphization of material takes place in the region under high compressive stress. The rolling and moving speeds of the abrasive have a combined influence on the distribution of the subsurface damages. A symmetrically distributed amorphous damage layer with a thinner thickness can be achieved when the rolling speed is less than the moving speed. In addition, the polishing speed influences the polishing force, materials removal amount, and subsurface damages significantly. The water environment is conducive to the ductile-mode material removal of the lutetium oxide crystal, increasing the plastic deformation of materials, such as the amorphization, and reducing the brittle damages, such as nanocracks.