In this article, we present a bifrequency acousto-optic beam splitter used to select independently the two polarization states of an arbitrary polarized input beam with two acoustic carriers. We make use of a dual frequency anisotropic interaction in the crystal, two acoustic waves diffract the optical beam, each frequency being tuned for interaction with only one of the beam polarizations. We explain how this double interaction is made possible by a proper cut of the paratellurite crystal and for a chosen launching angle of the input beam. In the first part we derive the theory underlying the acousto-optic interaction and the design of the paratellurite device. Then we describe our experimental setup, show some experimental results, and discuss them.