Mechanical metamaterials, artificial materials with counter-intuitive properties such as a negative Poisson’s ratio, not exhibited by conventional materials that is found in nature. Unusual properties of metamaterials are obtained from structural geometry, not their composition. Rational design of mechanical metamaterials at the micro- and macroscale is interesting as found novel geometries. However, incorporating movable building blocks inside solids, thereby enabling us to manipulate the mechanical movement at the molecular scale, has been a difficult task. Here we report a metal-organic framework, self-assembled from a porphyrin linker and a new type of Zn-based secondary building unit, acted as a joint in hinged cube tessellation. We show that this material is indeed mechanical metamaterial, exhibiting auxetic behaviour through detailed structural analysis and theoretical calculation. This work demonstrates that the topology of the framework and flexible hinges inside the structure are intimately related to the mechanical properties of the material, providing a guideline for the rational design of mechanically responsive metal-organic frameworks.