In this paper, a double-layer acoustic metasurface (DAM) composed of a fixed lower acoustic metasurface (LAM) and a rotatable upper acoustic metasurface (UAM) is proposed for the generation of mode-reconfigurable acoustic orbital angular momentum (OAM). The UAM and LAM are divided into multiple sections, in which the hybrid structures combining cascaded Helmholtz resonators and a straight pipe are adopted to achieve specific phase compensation. By rotating the UAM, the incident acoustic plane wave can be efficiently converted into the vortex acoustic waves of reconfigurable topological charges ranging from −5 to +5 with distinguishable purity. Furthermore, the influences of the parameters on the purity of the generated topological charges have been investigated and discussed, such as the distance between LAM and UAM, rotatable angle error, and operating frequency. With the capability of reconfigurable OAM modes, the proposed DAM can be used to efficiently increase capacity or to conveniently switch between different channels in underwater vortex acoustic communications.