The oxidation of aqueous solutions containing Allura Red AC (AR–AC) using bicarbonate-activated peroxide (BAP) and cobalt-impregnated pillared clay (Co/Al–PILC) as the catalyst was investigated. Using the CCD-RMS approach (central composite design–response surface methodology), the effects of dye, H2O2, and NaHCO3 concentrations on AR–AC degradation were studied. The decolorization, total nitrogen (TN), and total carbon (TC) removals were the analyzed responses, and the experimental data were fitted to empirical quadratic equations for these responses, obtaining coefficients of determination R2 and adjusted-R2 higher than 0.9528. The multi-objective optimization conditions were [dye] = 21.25 mg/L, [H2O2] = 2.59 mM, [NaHCO3] = 1.25 mM, and a catalyst loading of 2 g/L. Under these conditions, a decolorization greater than 99.43% was obtained, as well as TN and TC removals of 72.82 and 18.74%, respectively, with the added advantage of showing cobalt leaching below 0.01 mg/L. Chromatographic analyses (GC–MS and HPLC) were used to identify some reaction intermediates and by-products. This research showed that wastewater containing azo dyes may be treated using the cobalt-catalyzed BAP system in heterogeneous media.