We investigate the unique mechanical properties of reentrant 3D origami structures based on the Tachi-Miura polyhedron (TMP). We explore the potential usage as mechanical metamaterials that exhibit tunable negative Poisson’s ratio and structural bistability simultaneously. We show analytically and experimentally that the Poisson’s ratio changes from positive to negative and vice versa during its folding motion. In addition, we verify the bistable mechanism of the reentrant 3D TMP under rigid origami configurations without relying on the buckling motions of planar origami surfaces. This study forms a foundation in designing and constructing TMP-based metamaterials in the form of bellowslike structures for engineering applications.