Non-orthogonal multiple access (NOMA) is emerging as a promising, yet challenging, multiple access technology to improve spectrum utilization for the fifth generation (5G) wireless networks. In this paper, the application of NOMA to multicast cognitive radio networks (termed as MCR-NOMA) is investigated. A dynamic cooperative MCR-NOMA scheme is proposed, where the multicast secondary users serve as relays to improve the performance of both primary and secondary networks. Based on the available channel state information (CSI), three different secondary user scheduling strategies for the cooperative MCR-NOMA scheme are presented. To evaluate the system performance, we derive the closed-form expressions of the outage probability and diversity order for both networks. Furthermore, we introduce a new metric, referred to as mutual outage probability to characterize the cooperation benefit compared to non cooperative MCR-NOMA scheme. Simulation results demonstrate significant performance gains are obtained for both networks, thanks to the use of our proposed cooperative MCR-NOMA scheme. It is also demonstrated that higher spatial diversity order can be achieved by opportunistically utilizing the CSI available for the secondary user scheduling.