In this paper, we propose a new simultaneous information relaying and jamming (SIRJ) scheme based on a dual-functional reconfigurable intelligent surface (RIS) to achieve secure non-orthogonal multiple access communications. Specifically, the RIS elements are split into two groups, where elements in one group perform signal reflection to enhance the legitimate reception quality while elements in the other group generate artificial jamming to interfere with the eavesdropper (Eve). Based on different channel state information (CSI) availabilities of Eve, the system sum-rate is maximized by jointly optimizing the transmit beamforming of the base station, reflect beamforming of the RIS, and mode selection of each RIS element, subject to a maximum tolerable information leakage to Eve. For the case with perfect Eve’s CSI, a penalty based alternating algorithm is proposed to deal with the challenging multivariate coupled and mixed integer non-convex optimization problem. For the case with imperfect Eve’s CSI, we consider the infinite number of secrecy constraints, for which the traditional$\mathcal {S}$-procedure cannot be directly applied. To tackle this challenge, we devise an efficient transformation that fits the$\mathcal {S}$-procedure to the problem and propose a robust secure beamforming design. Simulation results demonstrate the performance advantage of the proposed SIRJ scheme over the existing baseline schemes.