In our previous work, a scale-up fabrication approach to cost effectively manufacturing nano-gratings over large area has been developed through diamond turning by using a multi-tip diamond tool fabricated by Focused Ion Beam. The objective of this study is to gain an in-depth understanding of the mechanism of machining nanostructures on single crystal copper through diamond turning when using a single tip and a multi-tip nanoscale diamond tool. For this purpose atomistic models of a single tip tool for multi-pass cutting and a multi-tip tool for single-pass cutting were built, respectively. The nature of the cutting chip formation, dislocation nucleation and propagation, cutting forces, and temperature distribution during nanometric cutting processes were studied through molecular dynamics (MD) simulations. Results show that nanostructure generation process at steady cutting stage was governed by a strong localization of the dislocation movement and the dynamic equilibrium of chip-tool contact area. Except the apparent improvement of machining efficiency that proportional to the tool tip numbers, the nano-grooves generated by multi-tip tool also have higher center symmetry than those machined by single tip tool. While the average tangential cutting force per tip were calculated all around 33.3 nN, a larger normal cutting force per tip being 54.1 nN was observed when using a multi-tip tool. A concept of atomistic equivalent temperature was proposed and used to analysis the important features of temperature distribution during the machining process. The advantage, disadvantage and applicability of diamond turning using multi-tip tool were discussed in comparison with those of using single-tip tool. The findings suggest that diamond turning using multi-tip tool might be more applicable than using single tip tool when apply to scale-up fabrication of periodic nanostructures.