Acoustic metasurfaces provide useful wavefront shaping capabilities, such as beam steering, acoustic focusing, and asymmetric transmission, in a compact structure. Most acoustic metasurfaces described in the literature are transmissive devices and focus their performance on steering sound beam of the fundamental diffractive order. In addition, the range of incident angles studied is usually below the critical incidence predicted by generalized Snell's law of reflection. In this work, we comprehensively analyze the wave interaction with a generic periodic phase-modulating structure in order to predict the behavior of all diffractive orders, especially for cases beyond critical incidence. Under the guidance of the presented analysis, a broadband reflective metasurface is designed based on an expanded library of labyrinthine acoustic metamaterials. Various local and nonlocal wavefront shaping properties are experimentally demonstrated, and enhanced absorption of higher order diffractive waves is experimentally shown for the first time. The proposed methodology provides an accurate approach for predicting practical diffracted wave behaviors and opens a new perspective for the study of acoustic periodic structures. The designed metasurface extends the functionalities of acoustic metasurfaces and paves the way for the design of thin planar reflective structures for broadband acoustic wave manipulation and extraordinary absorption.