The hemocyanin protein binds and transports molecular oxygen via two copper atoms at its core. The singlet state of the Cu2O2 core is thought to be stabilised by a superexchange pathway, but detailed in situ computational analysis is complicated by the multi-reference character of the electronic ground state. Here, electronic correlation effects in the functional site of hemocyanin are investigated using a novel approach, treating the localised copper 3d electrons with cluster dynamical mean field theory. This enables us to account for dynamical and multi-reference quantum mechanics, capturing valence and spin fluctuations of the 3d electrons. Our approach explains the stabilisation of the experimentally observed di-Cu singlet for the butterflied Cu2O2 core, with localised charge and incoherent scattering processes across the oxo-bridge that prevent long-lived charge excitations. This suggests that the magnetic structure of hemocyanin is largely influenced by the many-body corrections.