Abstract: The catastrophe of chip flow angle (CFA) is a phenomenon that is difficult to explain by traditional metal cutting theory, and has a great influence on the process effect. To reveal the inherent law of the CFA mutation phenomenon, a set of observation experiments on the critical cutting width of the CFA mutation were designed when the straight double-edged turning tool with different normal rake angles and the conical end face of 6061 aluminum alloy workpiece were traversed with varying rates of feed. The catastrophe of the CFA was captured by the video of the chip flow state, and the specific critical cutting width of the mutation was obtained. Taking the cutting width and cutting thickness (feed) as the control parameters, the CFA as the state variable, and the cutting power calculation function as the potential function, the cusp catastrophe mathematical model describing the catastrophe of CFA of 6061 aluminum alloy conical workpiece with linear double-edged turning tool is established by using the catastrophe theory, and the critical cutting width of sudden change under the condition of given cutting thickness is predicted. Comparing the measured value of the critical cutting width with the theoretical prediction value, the error between the measured value and the theoretical prediction value is calculated to be 8.87%, which is significantly improved compared with the similar model established by the predecessors.