This work comprehensively studies both the photocatalytic degradation and the adsorption process of Congo red dye on the surface of a mixed-phase copper oxide–graphene heterostructure nanocomposite. Laser-induced pristine graphene and graphene doped with different CuO concentrations were used to study these effects. Raman spectra showed a shift in the D and G bands of the graphene due to incorporating copper phases into the laser-induced graphene. The XRD confirmed that the laser beam was able to reduce the CuO phase to Cu2O and Cu phases, which were embedded into the graphene. The results elucidate incorporating Cu2O molecules and atoms into the graphene lattice. The production of disordered graphene and the mixed phases of oxides and graphene were validated by the Raman spectra. It is noted from the spectra that the D site changed significantly after the addition of doping, which indicates the incorporation of Cu2O in the graphene. The impact of the graphene content was examined with 0.5, 1.0, and 2.0 mL of CuO. The findings of the photocatalysis and adsorption studies showed an improvement in the heterojunction of copper oxide and graphene, but a significant improvement was noticed with the addition of graphene with CuO. The outcomes demonstrated the compound’s potential for photocatalytic use in the degradation of Congo red.