The mechanism of material removal process at the nanoscale lays the foundation for nanomachining technology. There are two major material removal mechanisms in cuffing: extrusion and shear. Though the shear theory has been successful in describing the conventional macro cutting methods, it may not be suitable for understanding the material removal at the nanoscale. As an alternative, the extrusion model was proposed for nanometric cutting. However, the concept of extrusion remains ambiguous, and the differences between extrusion and shear have not been fully clarified. In this research, molecular dynamics is performed to study material removal under various cutting conditions. Novel analysis methods are developed to characterize the nanocutting process for numerical simulation. The fundamental processes of extrusion and shear are successfully revealed. Chip formation and subsurface damage evolution are clearly interpreted. In addition, the variation in material removal with the sharpness of the cutting tool is analyzed. The results are significant for the development of the cutting theory.