Herein, the non-collinear acousto-optical two-stage diffraction of Bessel light beams by ultrasound in uniaxial gyrotropic crystals is theoretically and experimentally investigated. It is established that when Bessel light beams propagate along the optical axis of the crystal, the diffracted light beams of the ±1-th orders arrange symmetrically to the incident beam and have virtually the same intensity. When a Bessel light beam falls at the Bragg angle and near the optical axis, the two-stage Bragg diffraction is also observed, but the intensities of the diffracted beams of the +1-th and +2-th orders differ significantly from each other.