A general design paradigm for a novel type of acoustic metasurface is proposed by introducing periodically repeated supercells on a rigid thin plate, where each supercell contains multiple cut-through slits that are filled with materials possessing different refractive indices but the same impedance as that of the host medium. When the wavelength of the incident wave is smaller than the periodicity, the direction of the transmitted wave with nearly unity transmittance can be chosen by engineering the phase discontinuities along the transverse direction. When the wavelength is larger than the periodicity, even though the metasurface is impedance matched to the host medium, most of the incident energy is reflected back and the remaining portion is converted into a surface-bound mode. We show that both the transmitted wave control and the high reflection with the surface mode excitation can be interpreted by a unified analytic model based on mode-coupling theory. Our general design principle not only supplies the functionalities of reflection-type acoustic metasurfaces, but also exhibits unprecedented flexibility and efficiency in various domains of wave manipulation for possible applications in fields like refracting, collimating, focusing or absorbing wave energy.