We performed molecular dynamics simulations to study the nano-grinding process of copper-silicon with a single diamond abrasive grain. The Cu-Si model was based on the modified embedded-atom method. The effects of grinding depth, speed, and Cu thickness on material removal, defects, grinding forces, and temperature were analyzed based on dislocations and phase transitions. Our results show that effects of the interface emerge at a 4.3-nm Cu layer. Shockley dislocations extend from the ground surface to the Cu-Si interface, accompanied by formation of hexagonal-close-packed (HCP) Cu. Shockley dislocations, which lead to the HCP transition, clearly increase at a grinding depth of 4.3 nm. The phase transitions from the face-centered cubic to body-centered cubic structures are accompanied by an increase in the atomic kinetic energy. Kinetic energy is released as material recovers from elastic deformation. At high absorbed energies of 7.3 eV/atom potential and 4.4 eV/atom kinetic, the HCP structure is formed between the body-centered cubic and face-centered cubic phases. For the thinner Cu layer (2.2 nm), as the grinding depth gets closer to the Cu-Si interface, more chips form, causing the tangential forces to increase sharply, whereas the normal forces remain almost unchanged. Within a grinding speed range of 40 and 120 m/s, there is a linear positive correlation between the grinding temperature and the speed. The workpiece temperature rises by approximately 30 K for every 20 m/s increase in the speed.