Plasmon-induced transparency (PIT) is a class of electromagnetically induced transparency phenomenon that enhances the interaction between light and matter, thereby improving the performance of nano-optical devices. However, traditional PITs usually rely on near-field coupling between bright modes and dark modes. In order to break through the limitation of this mechanism, in this study we propose a dual-polarized graphene hypersurface structure, which consists of four groups of symmetric L-shaped graphene surrounding cross-shaped hollow graphene, forming a triple PIT through the synergistic effect between two single PITs. The accuracy of the results is verified by simulating the transmission spectra using the finite-difference time-domain, which is highly similar to that of the coupled-mode theory results. It is found that by modulating the Fermi energy levels and carrier mobility, this structure exhibits a group refractive index of up to 500 as a slow-light device, demonstrating excellent slow-light control capability. As a polarizing device, this structure has dual polarization characteristics and can generate a triple PIT window under both x and y polarized light incidence. In particular, the resonant frequency f₆ is not affected by the direction of polarization of the incident light. This good stability and resistance to interference in various polarized light conditions are particularly important for designing polarization devices. Meanwhile, we adjust the length parameter of graphene L₂ and find that the resonance frequency f₆ is still highly stable, showing a better tolerance to structural changes. Therefore, in this study, a multifunctional integrated device with slow light modulation and polarization selection in one device is designed, providing new theoretical guidance and research directions for synergistic effects based on polarization insensitivity.