Potential eavesdropping and malicious jamming attacks pose an enormous threat to wireless communication. In this paper, a novel architecture of reconfigurable intelligent surface (RIS)–simultaneously transmitting and reflecting (STAR)-RIS is utilized to assist both anti-jamming and anti-eavesdropping transmissions. We aim to minimize the access point (AP) transmit power while ensuring that both secure communication requirements and user service requirements are met. Since the channel status information (CSI) of illegal nodes (eavesdropper and jammer) is difficult to obtain accurately and the beamforming strategy of a jammer is unknown, we consider a robust beamforming design with imperfect CSI for illegal channels and an unknown jamming strategy. Outage-constrained power minimization problems are formulated for three different protocols of the STAR-RIS, namely, energy splitting (ES), mode switching (MS) and time switching (TS). For each protocol, the alternate optimization (AO)-based method is proposed to jointly optimize the active beamforming (ABF) of the AP and the passive beamforming (PBF) of the STAR-RIS to solve these nonconvex and highly coupled problems. Simulation results show the effectiveness of the proposed methods. Compared with the conventional RIS, the STAR-RIS has significantly more potential in terms of anti-jamming and eavesdropping suppression.