<p>Robotic mirror-milling is a promising technology for machining thin-walled parts. However, its further development is hindered by milling-induced vibrations. Accurate prediction and suppression of these vibrations require a reliable structural dynamic model of the robot, whose coefficient matrices are generally asymmetric. Although these matrices can be identified using Frequency Response Function (FRF) fitting, existing algorithms are often computationally inefficient. To overcome this limitation, a mode-shape-based fast FRF-fitting algorithm is proposed to identify the asymmetric dynamic model of the robot for milling stability prediction. First, an FRF matrix is derived from the asymmetric robot dynamic model. Both qualitative and quantitative mode-shape-based methods are developed to construct the coefficient matrices. Subsequently, a fast FRF-fitting algorithm is established by integrating a block coordinate descent strategy with a random scaling approach. The identified robot dynamics are then incorporated into a modified full-discretization method (FDM) framework for milling stability prediction. Finally, various coefficient-matrix formulations and identification algorithms are compared through simulations and robotic mirror-milling experiments.</p>