Non-radicals generated in peroxymonosulfate (PMS)-based Fenton-like catalysis exhibit rapid degradation of pollutants, yet the elucidation of structure–activity relationships and mechanisms remains challenging. Herein, a core–shell-like nitrogen-doped carbon-coated Co/MnO nanoparticle (Co/MnO@NC) based on bimetallic ZIF-L was constructed. Experimental studies and density functional theory (DFT) calculations show that the synergistic effect of bimetals can effectively reduce the d-orbital occupancy of the metal active center and the reaction energy barrier of O-O bond in PMS, thereby promoting the generation of high-valent metal-oxo and 1O2. The catalyst-PMS system achieved high sulfamethoxazole removal efficiency with a kobs value of 1.6526 min−1, which was 9 times higher than that of Co@NC. After integrating the Co/MnO@NC-loaded sponge into a continuous flow reactor, it effectively purified 20 L of SMX wastewater within 3 h, further underscoring the potential practicality of the catalyst. This work provides a feasible strategy and a theoretical model for the non-radical generation of a bimetallic catalyst-PMS system.