From the perspective of information security, relays exhibit varying levels of trustworthiness when forwarding information. For screening and eliminating the malicious users of cooperative NOMA relay networks, a reputation-based algorithm is proposed, in which the user relays (URs) are categorized into three types based on their behaviors—malicious users, speculative users, and honest users. Meanwhile, in order to minimize information leakage at the relay, cooperative interference signals are transmitted by far user (FU) and near user (NU) via the uplink while the base station (BS) is also transmitting signals to the relay. This approach increases inter-user interference (IUI) to confuse the eavesdropping capability of the relay. To verify the superiority of the proposed scheme, an asymptotic lower bound expression for the ergodic secrecy rate (ESR) of the downlink is derived to characterize the secrecy performance of the proposed scheme. Furthermore, in the case of limited system power, a joint power allocation algorithm based on the golden section method is also proposed to further enhance the security performances of the system. The simulation results validate the accuracy of the derived analysis results and demonstrate that the proposed scheme has a significant improvement in the ESR compared with the traditional scheme.