In this paper, a graphene plasmonic waveguide consisting of Si graded gratings and a SiO2 separator has been designed in order to rainbow trap and release in the mid-infrared frequencies. Tunability of the light trapping and releasing in this proposed structure has been realized thanks to the adjustable chemical potential of the graphene. Using this structure, the light velocity has been decreased by a slowdown factor above 1270 with a trapping bandwidth of 3.5 µm. Due to the high tunability of this miniaturized structure, it can be used in a variety of applications including optical switches, buffers, and storages.