To systematically investigate the specific factors influencing cutting force variations in ultrasonic cutting of Nomex honeycomb materials with disc cutters, a comprehensive theoretical framework was developed. This framework incorporates cutting parameters like feed speed, cutting width, and ultrasonic amplitude to establish a theoretical cutting force formula. Through an analysis of ultrasonic vibration-assisted cutting motion trajectories with a disc cutter, a microscopic model of material removal for Nomex honeycomb cutting was developed. This model decouples the isotropic motion of the disc cutter, yielding theoretical cutting force formulas for different directions, elucidating the reduction in cutting force under ultrasonic influence in both the vibration and feed directions. The formulated theoretical cutting force expressions were verified through ultrasonic cutting experiments. Results indicate that when cutting Nomex honeycomb materials with a disc cutter in the vibration direction, cutting force reduction arises from narrowing the effective cutting width between the tool and the material, and from intermittent contact that minimizes tool-material interaction time. A corresponding cutting force expression for this direction was established. In the feed direction, a mechanism similar to intermittent cutting with a straight blade is observed. Ultrasonic vibration's impact stress induces tensile stress in the uncut section, prompting microcrack propagation in the material's front end and reducing fracture stress, thus diminishing the cutting force. A damage factor was introduced to establish the cutting force expression in the feed direction. Error analysis comparing theoretical and experimental cutting force values under varying parameters revealed average errors of 32%, 36%, and 23% for different feed speeds, ultrasonic amplitudes, and cutting widths. These findings provide theoretical backing for optimizing cutting parameters.