The magnetic stirred reactor has been widely used because of its good sealing performance. Particle image velocimetry experiments are performed in the square cross-section of a magnetic stirred reactor. The flow structure and time evolution law at specific frequencies are obtained by a dynamic mode decomposition method. The results show that the turbulence at the stirring-bar outlet is fully developed, but there is an attenuation structure at other locations. The flow is in an unstable equilibrium state, and the Reynolds number can only reflect the local characteristics. The high-energy flow structures are the vortex structures formed by periodic rotating flow, free surface vortices, and cyclic shear flow. Because of the coupling between the fluid and stirring bar, vibration of the stirring bar is generated. This paper provides a new solution for the analysis of the mixing process as well as a basis for understanding the flow mechanism of the magnetic stirred reactor.