Taking the paraxial Gaussian vortex beam as an example, the variation of magnetic spectral Stokes singularities of partially coherent beams is studied at the source plane and compared with electric spectral Stokes singularities of partially coherent beams. It is shown that at the source plane there exists magnetic and electric spectral Stokes singularities of partially coherent Gaussian vortex beams. By suitably varying the beam waist width and off-axis parameter, the motion, creation, and annihilation of magnetic and electric spectral Stokes singularities will take place. In comparison with the electric spectral Stokes singularities of partially coherent beams, they do not coincide and the topological charges are not the same. But there exists a certain symmetry, and in the process, they satisfy the topological relation.