Flexible metal-organic frameworks (MOFs) are materials of great current interest. A small class of MOFs show flexibility driven by reversible bonding rearrangements that lead directly to unusual properties. Cu-SIP-3 is a MOF based on the 5-sulfoisophthalate ligand, where the strong copper-carboxylate bonds ensure that the three-dimensional integrity of the structure is retained while allowing bonding changes to occur at the more weakly bonding sulfonate group leading to unusual properties such as the ultra-selective adsorption of only certain gases. While the integrity of the framework remains intact during bonding changes, crystalline order is not retained at all times during the transformations. X-Ray diffraction reveals that highly crystalline single crystals lose order during the transformation before regaining crystallinity once it is complete. Here we show how X-ray pair distribution function analysis can be used to reveal the mechanism of the transformations in Cu-SIP-3, identifying the sequence of atomic displacements that occur in the disordered phase. A similar approach reveals the underlying mechanism of Cu-SIP-3's ultra-selective gas adsorption.