An ultrafast and low-power slow light tuning mechanism based on plasmon-induced transparency (PIT) for two disk cavities aperture-coupled to a metal-dielectric-metal plasmonic waveguide system is investigated numerically and analytically. The optical Kerr effect is enhanced by the local electromagnetic field of surface plasmon polaritons, slow light, and graphene–Ag composite material structures with a large effective Kerr nonlinear coefficient. Through the dynamic adjustment of the frequency of the disk nanocavity, the group velocity is controlled between c/53.2 and c/15.1 with the pump light intensity increased from 0.41 MW/cm2 to 2.05 MW/cm2. Alternatively, through the dynamic adjustment of the propagation phase of the plasmonic waveguide, the group velocity is controlled between c/2.8 and c/14.8 with the pump light intensity increased from 5.88 MW/cm2 to 11.76 MW/cm2. The phase shift multiplication of the PIT effect is observed. Calculation results indicate that the entire structure is ultracompact and has a footprint of less than 0.8 μm2. An ultrafast responsive time in the order of 1 ps is reached due to the ultrafast carrier relaxation dynamics of graphene. All findings are comprehensively analyzed through finite-difference time-domain simulations and with a coupling-mode equation system. The results can serve as a reference for the design and fabrication of nanoscale integration photonic devices with low power consumption and ultrafast nonlinear responses.