CVD-grown graphene exfoliates relatively easily by the oxidation of the copper substrate, yet the inherent oxidation of the graphene-coated copper is conceptually fascinating and poorly understood. Here, we report the study of O2 and H2O adsorptions at the graphene/Cu(111) interface using ab initio calculations. We demonstrate that intercalation can occur at the interface, via oxidation (dissociative adsorption of oxygen) near the monolayer edge sites. Graphene/Cu(111) interface has a strong oxide formation tendency; lower activation barrier for O2 and H2O dissociation into surface oxygen and hydroxyls, respectively. Graphene adsorption energy on the oxidized surface was reduced by a factor of two (per C-atom). As rapid oxidation proceeds, molecular (H2O or O2) intercalation may also occur. We propose that O2 dissociation at the graphene edges as the first step for Cu(111) oxidation, following by H2O dissociation as the second step for the graphene delamination. While our results provide information on the decoupling of CVD-grown graphene, other important findings can also be extracted from the interaction between graphene edges and the metal surface.