In this study, a Cu–Ce@Az ozone catalyst with multiple active components was prepared through the impregnation method to treat purified terephthalic acid (PTA) wastewater, and characterized by X-ray diffraction, X-ray fluorescence spectroscopy, scanning electron microscopy, specific surface area analysis, X-ray energy spectroscopy, X-ray photoelectron spectroscopy, and other methods. The Cu–Ce@Az ozone catalyst had a developed pore structure with a large specific surface area and crystal structure. After calcination, the metallic elements Cu and Ce existed in the state of oxides CuO and CeO2. The effects of reaction time, solution pH, catalyst dosage, and ozone dosage on the catalytic oxidation performance of the Cu–Ce@Az ozone catalyst were studied. Adding tert-butanol reduced the removal rate of COD from the PTA wastewater through the catalytic oxidation system, which proves that a Cu–Ce@Az ozone catalyst treatment process of PTA wastewater follows the free-radical reaction mechanism. The results of 3D fluorescence spectroscopy analysis show that the organic matter in the PTA wastewater was converted into tryptophan organic matter and aromatic organic matter after the reaction of the catalytic oxidation system. Ultraviolet absorption spectroscopy analysis indicated that in unsaturated chemical bonds, some conjugated structures and benzene ring structures of organic matter in the PTA wastewater were destroyed.