The present work is first aimed at recovering graphite from carbon rods of waste zinc-carbon (Zn-C) batteries for applications such as wastewater treatment, in order to contribute to the development of a sustainable environment. Then, a composite material, cobalt-iron layered double hydroxide combination with reduced graphene oxide, and with subsequent Ag nanoparticles deposition via NaBH4 reduction method (Ag/CoFe-LDH/rGO) was prepared for the catalytic activity of Rhodamine B (RhB) and Safranine-O (SO) as model contaminants from aquatic media. The catalytic activity of RhB and SO by Ag/CoFe-LDH/rGO in the presence of NaBH4 was studied to model and optimize the process parameters (NaBH4 amount, reaction time, initial dye concentration (Co), and catalyst dosage) via central composite design (CCD)-response surface methodology (RSM). Also, an artificial neural network (ANN) model was developed to estimate the catalytic activity of each dye using an RSM data set. The catalytic activities of 99.54% and 99.96% were obtained for RhB and SO dyes, respectively, under the optimal conditions: NaBH4 amount 12.32 mM, reaction time 3.19 min, Co 33.46 mg/L, and catalyst dosage 1.24 mg/mL for RhB dye; NaBH4 amount 16.76 mM, reaction time 3.06 min, Co 15.10 mg/L, and catalyst dosage 1.46 mg/mL for SO dye. The optimum conditions of process parameters by ANN with gray wolf optimizer (GWO) were in good agreement with the points determined the RSM-CCD. These results demonstrate that RSM and ANN approaches can be applied practically and efficiently to maximize the catalytic activity of RhB and SO by Ag/CoFe-LDH/rGO in the existence of NaBH4. On the other hand, from the kinetic and thermodynamic studies, the positive activation enthalpy, ΔH# and the negative activation entropy, ΔS# values for each dye demonstrated that the catalytic performance was endothermic and less random at the solid/liquid interface.