A computational model using the discrete element method is presented to investigate the impact process of multiple micro-particles on a quartz crystal. It is shown that the impacts initiate median and lateral cracks that degrade the strength of the substrate material and facilitate material removal in subsequent impacts. Elemental materials are removed through breaking their contacts with all adjacent elements by crack propagation and intersection. A larger overlapping impact condition between two impacts is more efficient for material removal in the second impact, but a total overlap does not yield the maximum material removal. The number of micro-cracks and the thickness of the cracked layer left on the eroded specimen are also studied in relation to the impact conditions.