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The nonradical process in the peroxydisulfate (PDS) oxidation system is a promising method for antibiotic removal in water. In this study, CuO@CNT was successfully synthesized by a facile approach to catalyze PDS. The removal efficiency of the antibiotic sulfamethoxazole (SMX) was 90.6% in 50 min, and the stoichiometric efficiency (ΔSMX/ΔPDS) was 0.402. The very different degradation efficiency of common organic contaminants revealed the selective oxidation of the surveyed system. The process of 1O2 oxidation and the electron-transfer regime was exhibited by chemical quenching tests, electron paramagnetic resonance (EPR) determination, a UV–vis spectrophotometer, X-ray photoelectron spectroscopy (XPS) detection, and cyclic voltammetry (CV) measurements. Sustainable catalysis was promoted by the circulation between the surface electron-rich centers of Cu(II) and Cu(III). Dissolved oxygen (DO) and a metastable Cu(III) intermediate contributed to the generation of 1O2. Still, a portion of SMX was removed by the mildly activated PDS. Moreover, the influence factors (pH, dosage, water matrix) were examined, and suppressions were acceptable by common anions and real water. Distinguished from the radical process, unique intermediate products were ascertained via the theoretical calculation and liquid chromatography–mass spectrometry (LC-MS) detection. Furthermore, CuO@CNT showed a satisfactory activation ability in the cycling experiments. Overall, this study developed CNT to be a supporter of CuO, unveiled the mechanism of catalysis, and evaluated the application potential of the nonradical process. [ABSTRACT FROM AUTHOR]