Reduced graphene oxide loaded with an iron-copper nanocomposite was prepared in this study, using graphene oxide as a carrier and ferrous sulfate, copper chloride and sodium borohydride as raw materials. The obtained material was prepared for eliminating hazardous dye carmine and the binary dye mixture of carmine and Congo red. The process of carmine dye removal by the nanocomposite was modeled and optimized through response surface methodology and artificial intelligence (artificial neural network–particle swarm optimization and artificial neural network–genetic algorithm) based on single-factor experiments. The results demonstrated that the surface area of the nanocomposite was 41.255 m2/g, the pore size distribution was centered at 2.125 nm, and the saturation magnetization was up to 108.33 emu/g. A comparison of the material before and after the reaction showed that the material could theoretically be reused three times. The absolute error between the predicted and experimental values derived by using artificial neural network–particle swarm optimization was the smallest, indicating that this model was suitable to remove carmine from simulated wastewater. The dose factor was the key factor in the adsorption process. This process could be described with the pseudo-second-order kinetic model, and the maximum adsorption capacity was 1848.96 mg/g. The removal rate of the mixed dyes reached 96.85% under the optimal conditions (the dosage of rGO/Fe/Cu was 20 mg, the pH was equal to 4, the initial concentration of the mixed dyes was 500 mg/L, and the reaction time was 14 min), reflecting the excellent adsorption capability of the material.