Motivated by the high maneuverability and low power consumption requirements, using elastic components in the joints of robotic fish can improve thrust production and efficiency. However, the propulsive performance of the elastic mechanism cannot be satisfied over a wide range of frequencies. First, this article develops a robotic tuna with a novel passive flexible joint structure, which combines with the compliance features of the elastic component and the damper, so as to maintain an ideal amplitude and phase difference of the caudal fin, resulting in better swimming performance over multifrequency ranges. Moreover, a dynamic model for the robotic tuna is established based on Kane method. Thrust characteristic calculation and computational fluid dynamics method are applied to analyze the propulsion and vorticity characteristics. Simulated results show that the composite mechanism generates higher thrust production and stronger vortex structures. Finally, simulations and experiments validate the effectiveness of the proposed method. Experimental results demonstrate that the robotic tuna can achieve a maximum speed of 1.21 m/s (equivalent to 2.24 body lengths per second) and minimum cost of transport of 45.67 J/(m$\cdot$kg).