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The reaction mechanism of methanol/dimethyl ether (DME) carbonylation catalyzed by isomorphously substituted B-, Al-, and Ga-MOR zeolites (B/Al/Ga-MOR) was comparatively investigated by the density functional theory (DFT) calculations. The commonalities and differences between methanol and dimethyl ether as the reactant as well as among various MOR zeolites in the catalytic reaction pathways were disclosed, where one Si atom was substituted by B, Al or Ga at the 8-ring side pockets T3 sites or the 12-ring channels T4 sites of MOR. The results indicate that the insertion of CO into methoxy group to form acetyl groups follows the SN2 mechanism and is the rate-determining step in the carbonylation reactions. Under 473 K, either methanol or dimethyl ether is used as feedstock, the formed acetyl group prefers to interact with CH3O in methanol to form methyl acetate. The T3 sites show better carbonylation selectivity, whereas T4 sites display better trimethoxonium ions selectivity which favors the generation of aromatics and leads to the catalyst deactivation. Comparing with Al-MOR, the introduction of Ga and B at the T3 sites increases the free energy barriers of carbonylation, whereas the introduction of Ga and B in particular at the T4 sites can substantially increase the energy barriers of generating trimethyloxonium ions, which can effectively suppress the side reaction and improve the catalyst stability. This work contributes to the understanding of the catalytic roles of various acidic sites in different channels of the MOR zeolites and provides certain theoretical support for tailoring and designing efficient MOR zeolite catalysts for methanol/dimethyl ether carbonylation.