The material characteristics such as size effect are one of the most important factors that could not be neglected in cutting the material at nanoscale. The effects of anisotropic nature of single crystal materials in nano-cutting are investigated employing the molecular dynamics simulation. Results show that the size effect of the plastic deformation is based on different plastic carriers, such as the twin, stacking faults, and dislocations. The minimum uncut chip thickness is dependent on cutting direction, where even a negative value is obtained when the cutting direction is {110}<001>. It also determines the material deformation and removal mechanism (e.g., shearing, extruding, and rubbing mechanism) with a decrease in uncut chip thickness. When material is deformed by shearing, the primary shearing zone expands from the stagnation point or the tip of stagnation zone. When a material is deformed by extruding and rubbing, the primary deformation zone almost parallels to the cutting direction and expands from the bottom of the cutting edge merging with the tertiary deformation zone. The generated surface quality relates to the crystallographic orientation and the minimum uncut chip thickness. The cutting directions of {110}<001>, {110}<1-10>, and {111}<1-10>, whose minimum uncut chip thickness is relatively small, have better surface qualities compared to the other cutting direction.