We propose a total-internal-reflection optical switch with a Bragg reflector waveguide. Slowing light in a Bragg reflector waveguide gives us an extremely large change in the equivalent refractive index of the waveguide, which is increased by a factor of more than 10 near a cut-off wavelength. Slowing light is caused by the giant waveguide dispersion of a Bragg reflector waveguide. The proposed structure enables a large bending angle of over 40 degrees even for reasonable refractive index changes of waveguide materials. The calculated result shows a possibility of large-scale and compact cross-bar waveguide optical switches.