It is well known that diamond is one of the most ideal cutting tool for materials, but the rapid tool wear can make surface integrity of the machined surface decline sharply during the nanometric cutting process for a single crystal silicon. Thus, a research on the wear mechanism of the diamond tool is of tremendous importance for selecting measures to reduce tool wear so as to extend service life of the tool. In this paper, the molecular dynamics simulation is applied to investigating the wear of the diamond tool during nanometric cutting for the single crystal silicon. Tersoff potential is used to describe the CC and SiSi interactions, and also the Morse potential for the CSi interaction. The rake and flank faces are diamond (111) and (112) planes respectively. A new method, by the name of 6-ring, is proposed to describe the bond change of carbon atoms. This new method can extract, all the worn carbon atoms in diamond tool, whose accuracy is higher than the conventional coordination number method. Moreover, the graphitized carbon atoms in the diamond tool also can be extracted by the combination of these two methods. Results show that during the cutting process, the CC bond's breaking in the surface layer of the diamond tool leads to the transformation of hybrid structure of the carbon atoms at both ends of the broken bond, from sp3 to sp2. Following to the bond breaking, the bond angle between the surface carbon atoms increases to 119.3 whose hybrid structure has changed, and the length between nearest neighboring atoms quickly decreases to 0.144 nm, indicating that the space structure formed by these carbon atoms has changed from 3D net structure of diamond to plane structure of graphite. Hence, the carbon atoms in the tool surface whose space structure has changed due to bond breaking should be defined as worn carbon atoms, but not only the carbon atoms whose hybrid structure has changed. The structure defects at both edges of the diamond tool are much more serious, which make the energy of CC bonds at the edges weakened with the enhancement of defects. The bonds with lower energy are broken under the effect of high temperature and shear stress, which also produces the tool wear. The graphitization occurs at the tool of the cutting tool because the structure defects there are the most serious. The reconstruction of the carbon atoms with lower coordination number causes its neighboring region to produce serious distortion, which leads to easy breaking of CC bonds in this region.