Acoustic communication has been widely used underwater due to its relatively low loss. However, acoustic wave doesn’t have the physical properties of spin and polarization like electromagnetic wave, which makes it impossible to broaden the channel capacity by these ways. Meanwhile, orbital angular momentum provides a new option for acoustic communication as a new degree of freedom independent from time and frequency. In this case, vortex beams, which carry the orbital angular momentum, are attracting great attention for their potential application of making acoustic waves transfer more information at the same frequency. As one kind of the vortex beams, Bessel beams have the characteristics of highly-localized energy and non-diffraction. In this manuscript, an artificial structure plate with hollow Archimedes spiral grids has been designed to manipulate the phase of the output wave with different incident acoustic wave. The spacing between the spiral grid is equal to the wavelength corresponding to the fundamental frequency. The flexible manipulation of the acoustic Bessel beam’s phase and topological order assisted by this plate have been studied theoretically and numerically. Based on Huygens principle, the distribution of output acoustic field produced by the incident plane wave or Bessel beam which travel through the plate from the front or the back side is derived. The result shows that when the plane wave transmits the plate from the opposite directions, the outgoing Bessel beam with opposite topological order can be obtained separately; when Bessel beam transmits the plate from the opposite direction, the outgoing Bessel beam with ascending or reduced order can be obtained. When the working frequency increases to a multiple of the fundamental frequency corresponding to the artificial structure plate, the higher multiple phase and topological order manipulation for the incident wave can be obtained. Similar result can also be derived by increasing the spacing between the spiral grid to a multiple of the wavelength. The result of numerical simulation is consistent with the theoretical derivation. And the theory also applies to high-order Bessel beam. Therefore, acoustic Bessel beam with arbitrary topological order can be obtained by this way. This proposed method has possible potential to promote the application of orbital angular momentum in information transfer and information encoding and decoding.