Abrasive air jet (AAJ) machining is a non-traditional technology used to pattern microstructures on a wide variety of engineering materials. Understanding the material removal mechanisms and the formation of micro-channels produced by AAJ is essential for optimizing process parameters and enhancing machining quality. Therefore, this study develops and validates a discrete element model to simulate abrasive air jet machining of micro-channels on quartz crystals. It shows that the crack network, which consists of opening mode cracks and shearing mode cracks, contributes to the removal of target particles. Opening mode cracks dominate the material removal process. The histories of the number of newly generated cracks and newly removed target particles can be divided into three stages: an incubation stage, a transitional stage, and a stable stage. Both the number of newly generated cracks and the number of newly removed target particles first increase and then decrease as the machining process progresses. An indicator called the “contribution rate” is proposed, showing that damage accumulates in the target substrate during abrasive air jet machining. During the machining of micro-channels, erosion impression appears at first. As the width and depth of the erosion impressions increase, micro-channels gradually form.