Extensive studies have been carried out on vertical or horizontal impact cutting because they are both high-efficiency rock breaking methods, but little attention has been paid to impact cutting with simultaneous vertical and horizontal impact loads. In this work, we conducted numerical simulations to study the mechanism of compound vertical and horizontal impact (CVHI) cutting. Firstly, a finite element analysis model considering the strain rate effect was established, and the parameters of the rock were adjusted by fitting laboratory test data of granite. Then, the differences in the cutting process between conventional cutting and CHVI cutting were analyzed, and a series of simulations were conducted to research how the vertical impact load affects the cutting mode. Finally, other simulations were performed with different horizontal impact loads to reveal the reason for improving cutting efficiency. Due to the applied vertical impact load, the rock failure mode is transformed from the ductile mode into the brittle mode. Besides, the torsional impact load can speed up the cutting process by promoting the generation, propagation, and connection of cracks. Therefore, the cutting efficiency is significantly improved with the action of CVHI loads.