We perform first-principles quantum mechanical studies of dioxygen ligand binding to the hemocyanin protein. Electronic correlation effects in the functional site of hemocyanin are investigated using a state-of-the-art approach, treating the localised copper 3\emph{d} electrons with cluster dynamical mean field theory (DMFT) for the first time. This approach has enabled us to account for dynamical and multi-reference quantum mechanics, capturing valence and spin fluctuations of the 3\emph{d} electrons. Our approach explains the stabilisation of the experimentally observed di-Cu singlet for the butterflied Cu$2$O$2$ core, with localised charge and incoherent scattering processes across the oxo-bridge that prevent long-lived charge excitations, suggesting that the magnetic structure of hemocyanin is largely influenced by the many-body corrections. Our computational model is supported by agreement with experimental optical absorption data, and provides a revised understanding of the bonding of the peroxide to the di-Cu system \emph{in vivo}.