The utilization of low-cost and abundant oxygen (O2) as an oxidant in the activation of copper-exchanged zeolites is highly important for the direct, selective oxidation of methane to methanol at low temperatures. While two motifs of active sites, i.e., the [Cu2(μ-O)]2+ and [Cu3(μ-O)3]2+, have been experimentally observed in mordenite (MOR) zeolite, the mechanisms of their formation from the reaction of Cu-MOR with O2 are still unclear. In this study, we performed density functional theory (DFT) calculations for O2 activation over 2[Cu2]2+-MOR and [Cu3O]2+-MOR zeolites. For the reaction on the dicopper species, we found two possible reaction routes: O-O bond cleavage leading to (1) formation of a [Cu2(μ-O)]2+ active species and a trans-μ-1,2-peroxo-Si2 species and (2) simultaneous formation of two [Cu2(μ-O)]2+ active species neighboring to each other. These routes are both exothermic but require completely different O-O bond activation energies. For the reaction on the tricopper species, we suggest a peroxo-Cu3O species as the intermediate structure with two transition states (TSs) involved in the reaction. The first TS where a significant rearrangement of the tricopper site occurs is found to be rate-determining, while the second TS where the peroxo bond is cleaved results in a smaller activation barrier. This reaction, in contrast to the dicopper case, is slightly endothermic. The present study provides theoretical insights that may help design of better Cu-exchanged zeolite catalysts for methane hydroxylation to methanol.