In this paper, a tunable arc-shaped acoustic metasurface (AAM) carpet cloak has been proposed and systematically investigated. The AAM carpet cloak consists of covers, rotors, bolts and nuts. The rotors can be rotated continuously within the covers to form a reconfigurable hook channel mechanism. By setting various rotational angles, we construct two-dimensional (2D) tunable AAM carpet cloaks to achieve excellent stealth performances under different operating conditions. Numerical simulations and experimental results for the 2D carpet cloaks show good agreements. Furthermore, simulated results for three-dimensional (3D) carpet cloaks have demonstrated that tapered objects are successfully escaping from being detected. The tunable hook channel mechanism can be flexibly applied to arbitrarily curved metasurface carpet cloaks, making them closer to practical invisibility acoustic devices.