Understanding the complex interactions between the work material and abrasives is a difficult and hot topic during grinding of Gallium nitride (GaN) single crystals. In this work, molecular dynamics (MD) simulations of double-grits interacted grinding of GaN crystals were performed, and the grinding force, coefficient of friction, stress distribution, plastic damage behaviors, and abrasive damage were systematically investigated. The results demonstrated that interacted distance with both radial and transverse directions achieved better grinding quality than that with only one direction or single-grit grinding. The grinding force, grinding induced stress, subsurface damage depth, and abrasive wear increases as the transverse interacted distance increases. However, the influence laws of the interacted distance on atom number of phase transition and dislocation length are not distinct. Appropriate interacted distances between abrasives can decrease grinding force, coefficient of friction, grinding induced stress, subsurface damage depth, and abrasive wear during the grinding process. Grinding test combined with the cross-sectional TEM detection verified the reliability of the simulated damage behaviors, i.e. amorphous, high-pressure phase transition, dislocations, stacking faults, and lattice distortions. The results not only enhance the understanding of damage accumulation and material removal caused by the coupling actions of abrasives in grinding process, but also provide a feasible approach for the wheel design of ordered abrasives.