Nanoparticle (NP), as a kind of hard-to-machine component in nanofabrication processes, dramatically affects the machined surface quality in nano-cutting. However, the surface/subsurface generation and the plastic deformation mechanisms of the workpiece still remain elusive. Here, the nano-cutting of a single-crystalline copper workpiece with a single spherical embedded nanoparticle is explored using molecular dynamics (MD) simulations. Four kinds of surface/subsurface cases of nanoparticle configuration are revealed, including being removed from the workpiece surface, moving as a part of the cutting tool, being pressed into the workpiece surface, and not interacting with the cutting tool, corresponding to four kinds of relative depth ranges between the center of the nanoparticle and the cutting tool. Significantly different plastic deformation mechanisms and machined surface qualities of the machined workpiece are also observed, suggesting that the machined surface quality could be improved by adjusting the cutting depth, which results in a change of the relative depth. In addition, the nanoparticle also significantly affects the processing forces in nano-cutting, especially when the cutting tool strongly interacts with the nanoparticle edge.