This study investigates the prespecified-/finite-time stability for a class of memristor-based BAM neural networks (MBAMNNs) with discontinuity. By C-regular Lyapunov approach stability theories, some criteria are established to ensure that the switched MBAMNNs can achieve prespecified-/finite-time stabilization, which are independent of the initial states. Finally, some numerical examples demonstrate the effectiveness of the proposed criteria. This work provides a theoretical foundation for precise temporal control in complex neural networks.