The dynamic behavior of spectral Stokes singularities (vortices) of stochastic electromagnetic beams propagating through an astigmatic lens is studied based on the spectral Stokes parameters and complex spectral Stokes fields. It is found that there exist $S_{12}$ , $S_{23}$ , and $S_{31}$ spectral Stokes vortices. By suitably varying propagation distance, spatial correlation length, off-axis distance or astigmatic coefficient, the motion, creation, annihilation, and changes in the degree of polarization of $S_{12}$ , $S_{23}$ , and $S_{31}$ vortices, in particular, the inversion of handedness of $S_{12}$ vortices may take place. A comparison with the previous work is also made.