To safeguard legitimate users from potential malicious eavesdropping, this letter proposes a dynamic role switching scheme (RSS) in multi-UAV assisted secure communication networks, where each UAV is allowed to collect offloading data from ground users (GUs) or generate artificial noise to suppress eavesdropper users (EUs). Given the scarcity of on-board resources, UAVs are expected to accomplish missions as soon as possible. Therefore, a dichotomy and successive convex approximation (dichotomy-SCA) combined algorithm is further designed to minimize the mission completion time (MCT) by the joint optimization of role assignment, trajectory and jamming power of UAVs. Numerical simulations illustrate that the proposed algorithm can be fast converged within limited iterations and outperform the role fixed scheme (RFS) with a better system performance. Meanwhile, MCT can be greatly reduced with a comparable average secure rate (ASR) compared with ASR maximizing algorithm.