<p>Acoustic orbital angular momentum (OAM) provides an infinite set of orthogonal bases in Hilbert space and significantly boosts the link capacity and data transmission rate. High-capacity and low-crosstalk OAM detection within compact physical space is highly desired to effectively harness this spatial dimension of sound wave, but the existing mechanisms generally either operate only for finite OAMs with predetermined mode orders or rely on complicated active devices. Here, we propose a phase saddle point (PSP) transformation mechanism for distinguishing and demultiplexing acoustic OAM modes in a passive, mode-adaptive, high-efficiency, and high-accuracy paradigm. The phase mask characterized by a PSP in the specific area is created through the single-pass log-polar transformation without prior information of incident modes, whose interaction with incident vortex beams of different OAM modes will yield the translation of the stationary phase point and thereby generate the corresponding focused line spots at distinct lateral positions. We theoretically elucidate the mode-adaptive response of PSP transformation by deriving the quantitative relationship between the OAM order and line spot offset. This mode adaptability enables our mechanism to detect OAM of arbitrary mode orders and mode numbers with the inter-mode crosstalk being effectively suppressed, beyond attainable with the existing methods. The effectiveness of our proposed mechanism is validated by demonstrating several distinct examples of single-mode OAM sorting and multi-mode synthesized vortex beam demultiplexing. We anticipate this mode-adaptive methodology, designed for compact dimensions and featuring with low crosstalk and uniform efficiency, will find important applications in OAM information processing.</p>