Robotic machining is an effective method for processing complex inner cavities of spacecraft cabins. For the machining requirements of some narrow and deep cavity sections, an extension rod is attached to the robotic endeffector to enhance operational accessibility. While extending the machining coverage, the rod increases the dynamic compliance of the system and is highly prone to inducing machining chatter, which in turn impairs machining quality and efficiency. To address this problem, a structural design and parameter optimization method for a tunable-frequency tuned mass damper (TMD) is proposed, and a dynamic model integrating the tuned mass damper with the robotic machining system is established. This method achieves frequency tunability based on an eccentric crank-slider mechanism and realizes damping parameter regulation according to the principle of eddy current damping. Further dynamic compliance control experiments on the robotic machining system are carried out. The results show that the proposed method can reduce the peak value of end-effector dynamic compliance by 67.8%, significantly expanding the stable machining boundary.