Due to its advanced spectral efficiency and energy efficiency, reconfigurable intelligent surface (RIS) received considerable attention in recent years. In this paper, in order to provide a practical scenario, we investigate an RIS-aided multi-input multi-output non-orthogonal multiple access multi-cell network, where both inter-cell and inter-cluster interferences are mitigated by the signal-cancellation-based (SCB) design at RISs. The passive beamforming at RISs is designed, where the minimal required number of RIS elements for implementing the proposed SCB design is evaluated. Then, the outage probability is evaluated for further revealing the diversity orders and the high-signal-to-noise-ratio slopes of accessed users. Our numerical results indicate that the multi-cast case provides the best performance compared to the zero-forcing and maximum-ratio-transmission cases