For better understanding of the essential mechanisms of material removal at extremely small depth of cut and ductile-brittle transition in material removal process of monocrystalline silicon carbide, which is expected as a next generation semiconductor material for wide band gap, high-voltage and low-loss power devices, nanometric deformation behavior in three-point bending of defect-free monocrystalline silicon carbide is analyzed by molecular dynamics (MD) computer simulation. The MD simulation results show that plastic deformation takes place through a phase transformation from cubic zinc sulfide to amorphous structures. The critical octahedral shearing stress for phase transformation is estimated to be 24 to 38 GPa. In the deformed region, a crack nucleus in atomic scale can be generated due to thermally activated vibration of atoms. After the crack nucleus, the crack extension takes place under certain stress field. The crack initiation takes place when a tensile stress reaches a certain critical value of approximately 67 GPa at the crack nucleus. The critical values for plastic deformation and crack initiation depend on crystal orientation and hydrostatic pressure. The results also show that there can be a number of critical criteria of the stress field to determine which processes plastic deformation or crack initiation predominantly takes place. When the plastic deformation proceeds to a crack initiation, ductile mode machining can be realized.