The process of gear chamfering and deburring is widely employed in manufacturing to remove burrs or smooth sharp edges from gear parts using a specialized tool, thereby reducing burrs and minimizing stress concentration on the tooth surface. In recent years, gear chamfering and deburring have become an indispensable process in high-performance gear manufacturing for new energy vehicles and industrial robots. This study presents a novel skiving method for chamfering and deburring cylindrical gears based on the principle of tooth profile generation by a cutting tool edge. A mathematical model is proposed to calculate the cutting edges of chamfering tool for skiving gear tooth profile. By developing an evaluation method for chamfering results, the influence of tool parameters on chamfering results is discussed. Experimental skiving chamfer is conducted using two chamfering tools on a specialized machine. The obtained results demonstrate that the theoretical values are in good agreement with the experimental values, with an error rate of no more than 13%, confirming the validity of the proposed approach. These findings offer both theoretical support for optimizing cylindrical gear chamfering processes and guidance for designing skiving chamfer tools.