In this work, we numerically study propagation and excitation of surface waves on a resonant and anisotropic self-complementary metasurface in the microwave range. We show that the TE- and TM-polarized fundamental surface modes have identical dispersion relations in different directions of propagation. Moreover, it is demonstrated that anisotropy of the metasurface results in very different group velocities in two mutually orthogonal propagation directions for both polarizations, which allows unidirectional and localized dual-polarized excitation.