Nonradical-based advanced oxidation processes for pollutant removal have attracted much attention due to their inherent advantages. Herein we report that magnesium oxides (MgO) in CuOMgO/Fe<sub>3</sub>O<sub>4</sub> not only enhanced the catalytic properties but also switched the free radical peroxymonosulfate (PMS)-activated process into the <sup>1</sup>O<sub>2</sub> based nonradical process. CuOMgO/Fe<sub>3</sub>O<sub>4</sub> catalyst exhibited consistent performance in a wide pH range from 5.0 to 10.0, and the degradation kinetics were not inhibited by the common free radical scavengers, anions, or natural organic matter. Quantitative structure-activity relationships (QSARs) revealed the relationship between the degradation rate constant of 14 substituted phenols and their conventional descriptor variables (i.e., Hammett constants σ, σ<sup>-</sup>, σ<sup>+</sup>), half-wave oxidation potential (<i>E</i><sub>1/2</sub>), and p<i>K</i><sub>a</sub> values. QSARs together with the kinetic isotopic effect (KIE) recognized the electron transfer as the dominant oxidation process. Characterizations and DFT calculation indicated that the incorporated MgO alters the copper sites to highly oxidized metal centers, offering a more suitable platform for PMS to generate metastable copper intermediates. These highly oxidized metals centers of copper played the key role in producing O<sub>2</sub><sup>•-</sup> after accepting an electron from another PMS molecule, and finally <sup>1</sup>O<sub>2</sub> as sole reactive species was generated from the direct oxidation of O<sub>2</sub><sup>•-</sup> through thermodynamically feasible reactions.