A combination of variable-temperature and variable-pressure single-crystal and powder X-ray diffraction is used to study the thermo- and piezo-mechanical properties of the metal-organic framework (MOF) silver(I) 2-methylimidazolate, Ag(mim). We find the material to exhibit a number of anomalous mechanical properties: negative thermal expansion, colossal positive thermal expansion and the most extreme negative linear compressibility yet observed for a MOF. By considering the mechanical response of individual supramolecular motifs we are able to rationalise the varied and unconventional behaviour of the bulk material. A general inverse correspondence between strength of supramolecular interaction and magnitude of mechanical response is identified. We propose that the consideration of MOF structures in terms of their underlying mechanical building units provides a straightforward qualitative method of directing framework design in order to maximise anomalous mechanical response.