When ultrasonically cutting honeycomb core curved parts, the tool face of the straight blade must be along the curved surface’s tangent direction at all times to ensure high-quality machining of the curved surface. However, given that the straight blade is a nonstandard tool, the existing computer-aided manufacturing technology cannot directly realize the above action requirement. To solve this problem, this paper proposed an algorithm for extracting a straight blade real-time tool face vector from a 5-axis milling automatically programmed tool location file, which can realize the tool location point and tool axis vector conversion from the flat end mill to the straight blade. At the same time, for the multi-solution problem of the rotation axis, the dependent axis rotation minimization algorithm was introduced, and the spindle rotation algorithm was proposed for the tool edge orientation problem when the straight blade is used to machine the curved part. Finally, on the basis of the MATLAB platform, the dependent axis rotation minimization algorithm and spindle rotation algorithm were integrated and compiled, and the straight blade ultrasonic cutting honeycomb core postprocessor was then developed. The model of the machine tool and the definition of the straight blade were conducted in the VERICUT simulation software, and the simulation machining of the equivalent entity of the honeycomb core can then be realized. The correctness of the numerical control program generated by the postprocessor was verified by machining and accuracy testing of the two designed features. Observation and analysis of the simulation and experiment indicate that the tool pose is the same under each working condition, and the workpieces obtained by machining also meet the corresponding accuracy requirements. Therefore, the postprocessor developed in this paper can be well adapted to the honeycomb core ultrasonic cutting machine tool and realize high-quality and high-efficient machining of honeycomb core composites.