We design and present a switchable slow light rainbow trapping (SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel supports slow light states with extremely small group velocity ($v_g=2.1\times {10}^{6}c$), low group-velocity dispersion, and a broadband operation bandwidth (3.60–4.48 GHz, near 22% of bandwidth). These slow light states originate from the strong coupling between two counter propagating topological photonic states. Under a gradient magnetic field, different frequency components of a wave packet are separated and stored at different positions for a long temporal duration with high spatial precision (without crosstalk and overlap between the electric fields of different frequencies) to form SLRT. Besides, these SLRT states can be easily switched among the forbidden state, trapped state, and releasing state by tuning the external magnetic field. The results suggest that the topological photonic state can offer a precise route of spatial-temporal-spectral control upon a light signal and find applications for optical buffers, broadband slow light systems, optical filters, wavelength-division multiplexing, and other optical communication devices.