The theoretical description of the primary dioxygen (O2) binding and activation step in many copper or iron enzymes, suffers from the intrinsically electronic non-adiabaticity of the spin flip events of the triplet dioxygen molecule (3O2), mediated by spin-orbit couplings. In this work, we presented the early-stage ultrafast spin flip dynamics of O2 binding for a simplified monocopper complex, involving the coupled singlet and triplet electronic states. The on-the-fly trajectory surface hopping (TSH) simulations have identified the dynamical effects that may influence the mode of O2 coordination (end-on vs. side-on), and the electronic structures can be viewed as complexes of molecular O2 with Cu(i) or as Cu(ii)-superoxide compounds. In addition, significant spin flip events are obversed within the sub-picosecond regime. We hope this work may provide complimentary insights on the traditional interpretation of O2 binding on copper complexes and subsequent catalytic reaction mechanisms.