This study investigates the degradation of Ponceau S (PS), a commonly used azo dye, through the cobalt-catalyzed Co2⁺/H2O2/UV advanced oxidation process (AOP). Process optimization was performed using the Box–Behnken design (BBD) under the framework of response surface methodology (RSM). Key operational parameters, namely the Co(II) concentration, the hydrogen peroxide (H2O2) dosage, and the PS dye concentration, were evaluated to maximize degradation efficiency, as the chosen response, after one hour of irradiation. The statistical analysis of the experimental data produced a robust predictive model with a high coefficient of determination (R2 = 0.9655), confirming the model’s reliability. The model F value of 21.79 indicates that the model is statistically significant, with only a 0.03% probability that such a high F value could result from random noise. Among the tested variables, the initial PS concentration and the H2O2 dose were found to have a highly significant impact on the degradation efficiency. In contrast, the Co(II) concentration showed no significant effect whether in its linear, interaction, or quadratic forms. Regarding interaction effects, only the interaction between dye concentration and H2O2 dose was significant, and among the quadratic terms, only the H2O2 dosage showed a notable influence. Optimal conditions for maximum PS degradation were determined to be 0.03 mM dye concentration, 0.55 mM H2O2, and 0.06 mM Co2⁺. These findings underscore the potential of the Co2⁺/H2O2/UV system as an effective method for azo dye wastewater treatment, with BBD proving to be a valuable tool for operational optimization.