While drilling deep or ultra-deep wells in hard rock formations, there are significant problems such as easy wear of drilling cutters and a low rate of penetration (ROP), and rotary percussion drilling technology is one of the essential techniques for improving drilling efficiency. However, there is currently limited research on the compatibility of rotary percussion drilling tools, polycrystalline diamond compact (PDC) cutters, and hard rock formations. Considering the motion mechanism of rotary percussion drilling tools, a three-dimensional rock-breaking numerical model was established for different cutters (planar, axe-shaped, and triple-ridged) under impact loads. Penetration depths, cutting widths, and rock-breaking volumes of different cutters under static and dynamic load coupling were analyzed. Changes in tensile, compressive, and shear stresses during the cutter rock-breaking process were compared, revealing the different cutter rock-breaking mechanisms under impact loads. The cutter rock-breaking laws under different impact amplitudes and frequencies were analyzed quantitatively, and the differences in rock-breaking effects of different cutters under various geological conditions were assessed. The results indicated that cutter penetration depth during rotary percussion drilling could be increased by 16.04% compared to that during conventional drilling. Under the same impact load, the rock-breaking effects of different cutters on hard and soft rocks exhibited similar variation patterns. The penetration depth followed the order axe-shaped > triple-ridged > planar cutters, with an average tangential order of triple-ridged < axe-shaped < planar cutters. When drilling through hard rock, the average penetration depths of planar, axe-shaped, and triple-ridged cutters were 5.57, 6.06, and 3.91 mm, respectively. The average tangential forces were 670.57, 541.76, and 347.89 N, respectively. During the transition from soft to hard rock during drilling, the tangential forces of the planar, axe-shaped, and triple-ridged cutters increased by 8.41%, 3.21%, and 2.64%, respectively. The planar cutter experienced the most significant instantaneous tangential-force change and was more prone to impact damage. Increasing the amplitude of the axial stress waves helps enhance the penetration depth of the drill bit, whereas increasing the frequency of the stress waves can reduce the intensity of fluctuations during drill-bit penetration and increase drill-bit stability. The research results provide insights into optimizing drilling cutters and engineering parameters during rotary percussion drilling.