To address the problem of the poor stability of ultrasonic machining of wave-absorbing honeycomb materials, this paper takes ultrasonic cutting of wave-absorbing honeycomb materials with a disc cutter as the research object and establishes a multi-degree-of-freedom mathematical model of the cutting system based on the relative positions of the tool and the honeycomb material and the motion characteristics of the tool. On this basis, modal analysis of the disc tool and the honeycomb cellular element wall plate is carried out to draw the Lobe diagram of ultrasonic cutting stability, the process experimental parameters are determined according to the solved stability Lobe diagram, and machining stability verification experiments are carried out. The experimental results show that the machining parameters in the stable region of the Lobe diagram result in a neat and clean surface, less fibre pullout, a complete outer substrate, and less tool wear than those in the critical and unstable regions, thus verifying the correctness of the theoretical model and the stability Lobe diagram.