We report that extremely polarization-sensitive stimulated Brillouin scattering (SBS) emerges in subwavelength elliptical waveguides when mediated by surface acoustic waves. We find based on the full-vectorial finite element analysis that the SBS driven by a specific surface acoustic wave can be eliminated for one polarization mode, whereas for the other polarization mode, it is kept significant, while such strongly polarization-dependent Brillouin gain has not been observed in conventional SBS by bulk acoustic waves. We explain the origin of these intriguing polarization-selective phenomena in terms of the counter-balance between the photoelastic and moving-boundary effects. Our findings provide a host of unique possibilities of highly efficient all-optical control and stabilization of the polarization state of light. Published by AIP Publishing.