Aramid fiber-reinforced plastic (AFRP) is widely used in bullet-proof and armor structures, and is difficult to drill because of the high-toughness aramid fibers with ductile fracturing—differently from carbon fiber. Therefore, drilling quality cannot be ensured by the drilling used for carbon fiber-reinforced plastic, and frequently, delamination and burrs occur in the drilling process. This article first established a two-dimensional cutting model for analyzing the fiber deformation and material interface cracking. According to the model, reducing the thrust force and the radial force of the edge on the fibers is an effective way to reduce the fiber deformation, and a three-point step drill is proposed further. Comparative experiments were carried out among twist drilling, candle core drilling and three-point step drilling under three drilling parameters. The results show that the three-point step drill changed the traditional cutting behavior on the drill-exit material into a compound process. Finally, the AFRP was cut effectively with the novel drill with a small thrust force, and the delamination and “burrs area” were reduced through different drilling parameters. In summary, the three-point step drill can drill the AFRP without delamination and burrs with 0.02 mm/rev, which provides a new solution of cost-effective production for AFRP manufacturers.