Low-frequency chatter severely limits robotic milling efficiency. In this paper, tuned mass dampers (TMDs) are introduced to suppress low-frequency chatter based on robotic modal directionality. A TMD model with mounting angle is established, and the suppression effect of TMD on the robotic low-frequency dynamic compliance with different mounting directions is analyzed together with experiments. Then, low-frequency chatter is further suppressed by suppressing side-frequency dynamic compliance. The milling experiments show that the TMD can significantly suppress low-frequency chatter and improve cutting amount, and a better effect can be achieved when TMDs act at both the low-frequency mode and side frequencies.