The parallel track scraping principle of conventional PDC bits largely limits the cutting efficiency and working life in deep formations. Cross-cutting polycrystalline diamond compact (PDC) bit may be an efficient drilling tool that increases the rock-breaking efficiency through both cross-cutting and alternate-cutting modes of the PDC cutter. The motion track equation of the cross-cutting PDC bit was derived by using the compound coordinate system, and the motion track was analyzed. Meanwhile, through the unit experiment and discrete element simulation, the cutting force, volume-specific load, and crack propagation were analyzed under different cutting modes. Through establishing a nonlinear dynamic model of the bit-rock system, the speed-up mechanism of the novel bit was analyzed based on rock damage, rock stress state, and motion characteristic of the bit during the rock-breaking process. Compared with unidirectional cutting, cross-cutting produces less cutting force, more brittle fracture, and a greater decrease of formation strength. The novel PDC bit can put more rock elements into a tensile stress condition than a conventional PDC bit, and the plastic energy dissipation ratio of the cross-cutting PDC bit is lower while the damage energy consumption ratio is higher than they are for conventional bits, which is beneficial to increasing the ratio of fracture failure and improving rock-breaking efficiency. Laboratory drilling tests show that the cross-cutting PDC bit can create mesh-like bottom-hole features. Drilling contrast experiments show that a mesh-like bottom-hole pattern can be obtained by using the cross-cutting PDC bit, of which the ROP is obviously higher than that of the conventional bit when drilling in sandstone or limestone formation. Meanwhile, the influence of deviation angle, weight on bit, and rock properties on cutting efficiency of the cross-cutting PDC bit are studied.