The angle milling head, a specialized tool capable of expanding machining range and improving adaptability of machine tools, is extensively applied in the machining of complex aircraft structural components. However, its high length/diameter ratio often leads to low rigidity, making it highly susceptible to chatter during actual machining processes, which severely impacts machining efficiency and accuracy. A two-degree-of-freedom (two-DOF) tuned mass damper (TMD), externally mounted on the angle milling head with minimized structural modifications, is specifically designed for suppressing vibration of the angle milling head along two orthogonal axes and milling chatter. Based on experimental measurements of the angle milling head’s dynamics, a dynamic model for the angle milling head–TMD system is developed. Numerical optimization is then carried out to determine the optimal dynamic parameters for the TMD. A configuration design for the two-DOF TMD is performed using the graphical approach according to mode shapes of the angle milling head, followed by finite element simulations of the TMD prototype. Finally, modal tests and cutting experiments were conducted to validate effectiveness of the TMD. Experimental results demonstrate that after installation of the TMD, the maximum magnitude of the frequency response function measured at the end of the angle milling head decreased by 73.5%, while the stable cutting depth increased by 300% (from 0.4 mm to 1.6 mm at spindle speed of 1000 r/min).