Nowadays, for environmental remediation, photocatalytic process involving graphene-based semiconductors is considered a very promising oxidation process for water treatment. In the present study, nanocomposite (Cu/Ni/rGO) has been synthesized by Dypsis lutescens leaf extract. Characterization of the sample was carried out by UV-visible spectroscopy, scanning electron microscopy (SEM), energy dispersive X-ray (EDX) analysis, Fourier transform infrared spectroscopy (FTIR), and X-ray diffraction (XRD). Different parameters like contact time, nanocatalyst amount, dye concentration, effect of temperature. and pH factor were optimized to examine the maximum removal efficiency for dyes rhodamine B and alizarine R with and without visible light source. In both cases, i.e., with or without light, maximum removal was observed at 20 mg of nanocatalyst for 5 ppm concentration of both dyes at 45 °C temperature and pH 10 for rhodamine B and pH 4 for alizarine R, respectively with a 20 min contact time. Maximum removal of dyes 93% rhodamine B and 91% alizarine R were observed under a tungsten lamp as compared to without a tungsten lamp, i.e., 78% of RhB and 75% of AR from mixture solution of these dyes. To assess the rate of reaction, spontaneity, and nature of reaction thermodynamics, kinetics and adsorption isotherms were studied. Thermodynamic values indicated that both dyes depicted endothermic and spontaneous degradation processes. Isotherm data fitted best to a Freundlich isotherm, while results of kinetic studies of both dyes followed the pseudo 2nd order kinetic equation. In the end, scavenging radical studies concluded that hydroxyl radicals were the main active specie involved in the photocatalytic degradation process, and regeneration experiments resulted that Cu/Ni/rGO nanocomposites were re-utilized for about four times.