Surface plasmon polaritons have been extensively studied owing to the promising characteristics of near fields. In this paper, the cascade coupling of graphene surface plasmon polaritons (GSPPs) originating from cascading excitation and multiple coupling within a composite graphene-dielectric stack is presented. GSPPs confined to graphene layers are distributed in the entire stack as waveguide modes. Owing to the near-field enhancement effect and large lifetime of the GSPPs, the terahertz wave-graphene interaction is significantly enhanced, which induces an ultra-extraordinary optical transmission (UEOT) together with the reported negative dynamic conductivity of graphene. Furthermore, owing to cascade coupling, the UEOT exhibits considerable transmission enhancement, up to three orders of magnitude, and frequency and angle selections. Based on the key characteristics of cascade coupling, the mode density and coupling intensity of GSPPs, the dependences of the number of graphene layers in the stack, the thickness of dielectric buffers, and the effective Fermi levels of the graphene on the UEOT are also analyzed. The proposed mechanism can pave the way for using layered plasmonic materials in electric devices, such as amplifiers, sensors, detectors, and modulators.