An Mn/Ce@red mud (RM) catalyst was prepared from RM via a doping–calcination method. Scanning electron microscopy, X-ray diffraction, and X-ray photoelectron spectroscopy were used to characterize the surface morphology, crystal morphology, and elemental composition of the Mn/Ce@RM catalyst, respectively. In addition, preparation and catalytic ozonation conditions were optimized, and the mechanism of catalytic ozonation was discussed. Lastly, a fuzzy analytic hierarchy process (FAHP) was adopted to evaluate the degradation of coal chemical biochemical tail water. The best preparation conditions for the Mn/Ce@RM catalyst were found to be as follows: (1) active component loading of 3%, (2) Mn/Ce doping ratio of 2:1, (3) calcination temperature of 550 °C, (4) calcination time of 240 min, and (5) fly ash floating bead doping of 10%. The chemical oxygen demand (COD) removal rate was 76.58% under this preparation condition. The characterization results suggested that the pore structure of the optimized Mn/Ce@RM catalyst was significantly improved. Mn and Ce were successfully loaded on the catalyst in the form of MnO2 and CeO2. The best operating conditions in the study were as follows: (1) reaction time of 80 min, (2) initial pH of 9, (3) ozone dosage of 2.0 g/h, (4) catalyst dosage of 62.5 g/L, and (5) COD removal rate of 84.96%. Mechanism analysis results showed that hydroxyl radicals (•OH) played a leading role in degrading organics in the biochemical tail water, and adsorption of RM and direct oxidation of ozone played a secondary role. FAHP was established on the basis of environmental impact, economic benefit, and energy consumption. Comprehensive evaluation by FAHP demonstrated that D3 (with an ozone dosage of 2.0 g/H, a catalyst dosage of 62.5 g/L, initial pH of 9, reaction time of 80 min, and a COD removal rate of 84.96%) was the best operating condition.