Reconfigurable intelligent surfaces (RISs) is a novel communication technology that has been recently presented as a potential candidate for beyond fifth-generation wireless communication networks. In this paper, we propose a priority-aware user traffic-dependent grouping-based multihop routing scheme for a RIS-assisted millimeter wave (mmWave) device-to-device (D2D) communication network with spatially correlated channels. Specifically, the proposed scheme exploits the priority of the users (based on their respective delay-constrained applications) and the aspect of spatial correlation in the narrowly spaced reflecting elements of the RISs. Here, based on the other users in the neighborhood, their respective traffic characteristics, and the already deployed RISs in the surroundings, we establish a multihop connection for information transfer from one of the users to its intended receiver. In this context, we take into account the impact of considering practical discrete phase shifts at the RIS patches instead of its ideal continuous counterpart. Moreover, we also claim and demonstrate that the existing classic least remaining distance (LRD)-based approach is not always the optimal solution. Finally, numerical results demonstrate the advantages of the proposed strategy and that it significantly outperforms the existing benchmark schemes in terms of system performance metrics such as data throughput, energy consumption, as well as energy efficiency.