Dynamically controlling electromagnetic waves at will is highly desired in many applications, but most previously realized mechanically reconfigurable metasurfaces are of restricted wave-control capabilities due to the limited tuning ranges of structural properties (e.g., lattice constant or meta-atoms). Here, we present mechanically reconfigurable metasurfaces in which both lattice constants and local reflection phases of constitutional meta-atoms can be synchronously controlled based on the kirigami rotation transformation, thereby exhibiting extended tuning ranges and thus wave-control capabilities. In particular, such metasurfaces can exhibit continuously varied and even re-formed reflection-phase profiles along with the kirigami rotation transformation, serving as ideal platforms to achieve reconfigurable beam steering in pre-designed manners. Using this concept, we design and fabricate two kirigami metasurfaces, working as a beam flipper and as a beam splitter for microwaves, respectively, and experimentally characterize their wave-manipulation functionalities. Experimental results are in good agreement with full-wave simulations. The proposed idea is so general that it can be applied to realize reconfigurable metasurfaces with different materials/configurations or in high frequency regimes, for controlling electromagnetic waves and other classical waves (e.g., acoustic waves).