Facing the challenge of increasingly severe environmental issues, many researchers are committed to seeking "post lithium-ion batteries" that can replace fossil fuels, one of which is alkali-metal-oxygen batteries. Nevertheless, the main bottleneck restricting the development of these batteries is the need for suitable catalysts to facilitate the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). In this study, we attempt to modify the catalytic performance of δ-MnO2 for lithium- and sodium-oxygen batteries (LOBs and SOBs) by constructing 1,4-benzenedisulfonic acid, 2-chloro-1,4-benzenedisulfonic acid, and 2-fluoro-1,4-benzenedisulfonic acid pillared structures (H-, Cl-, and F-MnO2). Their dynamic stability and catalytic mechanism have been explored by employing density functional theory (DFT). H-MnO2 possesses a theoretical discharge voltage of 2.645 V for LOBs, which is 0.293 V larger than that of Cl-MnO2. The discharge voltage of Cl-MnO2 for SOBs is 3.152 V; however, H-MnO2 impedes the formation of sodium superoxide and can hardly promote the ORR in SOBs. Both H- and Cl-MnO2 can prevent the parasitic disproportionation reaction in LOBs and SOBs that produce active singlet oxygen through different reaction mechanisms. We believe that the constructed pillared structures are efficient ORR/OER catalysts for alkali-metal-oxygen batteries. Our research provides a theoretical basis for the micro-level mechanism of LOBs and SOBs catalyzed by the pillared δ-MnO2 and sheds light on ameliorating the properties of the catalyst by constructing pillared structures.