In this study, the authors use the partial-wave series expansion method in the spherical coordinate system and provide a theoretical formula for the off-axis acoustical scattering by rigid prolate and oblate spheroids illuminated by an arbitrary-order Bessel beam to explore the physical characteristics of the off-axis far-field scattering (the axis of the Bessel beam is parallel to the axis of the spheroids). The proposed method is verified and several three-dimensional far-field directivity patterns of rigid spheroids illuminated by zeroth- and first-order Bessel beams are depicted to explore the off-axis scattering. A special emphasis is placed on the geometry size of the prolate and oblate spheroids, the half-cone angle of the Bessel beam, the order of the Bessel beam, and the offset position. Compared with the on-axis scattering, the derivation and calculation of the off-axis scattering takes into account the spherical harmonic function using a numerical integral procedure. In addition, no symmetry was observed in the patterns of the far-field acoustic scattering form function for the zeroth- and higher-order Bessel beams with the off-axis illumination. This investigation provides a tool for the exploration of the complex scattering problems of underwater non-spherical particles under the illumination of the Bessel beam.