Towards the utilization of Cu2O nanomaterial for the degradation of industrial dye pollutants such as methylene blue and methyl orange, the graphene-incorporated Cu2O nanocomposites (GCC) were developed via a precipitation method. Using Hummers method, the grapheme oxide (GO) was initially synthesized. The varying weight percentages (1–4 wt %) of GO was incorporated along with the precipitation of Cu2O catalyst. Various characterization techniques such as Fourier-transform infra-red (FT-IR), X-ray diffraction (XRD), UV–visible diffused reflectance (UV-DRS), Raman spectroscopy, thermo gravimetric analysis (TGA), energy-dispersive X-ray analysis (EDX), and electro chemical impedance (EIS) were followed for characterization. The cabbage-like morphology of the developed Cu2O and its composites were ascertained from field-emission scanning electron microscopy (FESEM) and high-resolution transmission electron microscopy (HR-TEM). In addition, the growth mechanism was also proposed. The results infer that 2 wt % GO-incorporated Cu2O composites shows the highest value of degradation efficiency (97.9% and 96.1%) for MB and MO at 160 and 220 min, respectively. Further, its catalytic performance over visible region (red shift) was also enhanced to an appreciable extent, when compared with that of other samples.