A mixed Eulerian-Lagrangian discrete vortex method is developed for solving the shallow water flows. In this discrete vortex model, new vortices are generated not only at the boundaries, but also in areas where bed friction, Coriolis force, surface wind stresses, or depth gradient is present, and the vorticity transport equation is split into four parts: (1) the advective movement of potential vorticity. (2) the generation of vorticity due to bed friction, Coriolis force, surface wind stresses, or depth gradients. (3) the diffusion of vorticity due to viscosity. (4) the diffusion of vorticity due to dilation. The shallow water flows past a rectangular cylinder at high Reynolds number are simulated with the method, and the distribution of vortices and the velocity field are obtained. The flow separation and the consequential process of development of vortices are seen clearly from the gained results.