The structural and electronic properties of graphene coated on a Cu(111) surface can be strongly influenced by the arrangement of adsorbates at the graphene edges. Oxygen and water intercalation at the graphene edges could lead to oxidation and hydrolysis at the graphene/Cu(111) interface, eventually causing decoupling of graphene from the Cu substrate. However, the reaction pathways for oxygen or water (or both) intercalation at the graphene edges are not well understood at the molecular level. Using ab initio density functional theory calculations, we observed a strong hybridization of pi orbitals at a zigzag edge of a graphene nanoribbon (GNR) on a bare Cu(111) surface, whereas such hybridization was absent for the corresponding armchair edge under otherwise identical conditions. These results indicate that the edge type influences the oxidation chemistry beneath the GNR. Moreover, we demonstrate that the presence of oxygen species, as well as GNR, facilitates the propagation of H2O. The following decoupling mechanisms are discussed: (i) GNRs with armchair edge configurations on Cu(111) can be decoupled via a sequential reaction that involves O-2 dissociation followed by H2O intercalation, whereas (ii) GNRs with zigzag edge configurations on Cu(111) can be decoupled by oxygen intercalation.