A method is described for deflecting a microwave acoustic beam by controlling the group-velocity deviation in an anisotropic medium. The basic principle is presented in terms of a general wave-vector surface. A detailed treatment is then given for the special case of anisotropy due to the spin-acoustic-wave interaction in magnetic insulators. Experimental beam deflection observations in yttrium iron garnet are discussed. A brief discussion of beam deflection in current-carrying piezoelectric semiconductors is also given. Possible applications of this method of beam deflection are suggested.