The utilization of Special-shaped Polycrystalline Diamond Compact (SPDC) cutters improves the performance of PDC cutters and extends their lifespan. Researchers have extensively explored the rock-cutting mechanism of SPDC cutters. However, most existing studies view SPDC cutter cutting and penetration processes separately, resulting in the cutting depth not dynamically changing during the cutting process, which deviates from the actual drilling process. This study establishes a discrete element-based numerical model to simulate the fragmentation of heterogeneous granite using SPDC cutters. It comprehensively analyzes the rock-breaking characteristics of the SPDC cutters under combined penetration and cutting from multiple perspectives. The results show that for granite, the Stinger cutter (CS) has the best penetration effect, followed by the Axe-shaped cutter (AX), Cylindrical cutter (CY), and Three-blade cutter (TB) in descending order. Under combined penetration and cutting, CY demonstrates the highest comprehensive rock-breaking efficiency, followed by AX, TB, and CS. Under straight cutting, the rock primarily fails in tensile, and the cutting depth of each cutter linearly increases with the cutting distance. The expansion extent of cracks is a key factor affecting rock-breaking efficiency, with cracks tending to expand vertically, and the cutter shape has little impact on it. The rock debris predominantly consists of small-volume fragments, particularly noticeable with CS. When crushing granite, AX is suitable for working under a WOB of 1 kN, CY is recommended for 2 kN, TB is suitable for 3 kN, and CS achieves the best rock-breaking efficiency at 4 kN. The study provides new insights into the selection of PDC drill bits and the optimization of PDC cutter arrangements.