In recent years, the reconfigurable intelligent surface (RIS) has garnered considerable interest for its remarkable advancements in spectral efficiency (SE) and energy efficiency (EE). To further enhance the performance of cellular networks, we propose a novel RIS-aided multi-input multi-output (MIMO) non-orthogonal multiple access (NOMA) architecture. To mitigate both inter-cell and inter-cluster interferences, we introduce a signal-cancellation-based (SCB) design specifically tailored for the RISs. By strategically deploying the RIS in suitable locations and adjusting the reflection coefficient (RC) of its elements, we achieve effective interference mitigation. The passive beamforming at the RISs is meticulously designed, and we assess how many RIS elements are necessary to implement the SCB design. To gain insights into system performance, we analyze the outage probability and the ergodic rate, providing valuable information on the high signal-to-noise ratio slopes and diversity orders for the users in the network. The numerical results reveal: 1) in comparison to the zero-forcing and maximum-ratio-transmission precoding matrices, the identity precoding matrix at the BS offers superior performance; 2) an optimal number of RIS elements exists in order to maximize both SE and EE.