In this work, we described the synthesis of pure graphene sheets (≤5 layers) and graphene-copper nanocomposites by using the commercial microwave oven and L-ascorbic acid (LAA), as a cost effective and environmental friendly approach. The successful formation of composites, few layer graphene sheets (FLG) with copper nanostructures, was confirmed by the X-ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses. The optical studies of the prepared samples exhibited band-band transition related strong UV absorption and strong UV emission alone with no visible range emission that supported the successful formation of graphene sheets with insignificant surface functional groups. The observed luminescence quenching in the composites when compared with the pure graphene sheets was discussed. Further we demonstrated the usage of these composites as a catalyst for hazardous azo dye reduction. The comparative study of the pure graphene and graphene-copper composites in the reduction of azo dye showed that the composites exhibited a rapid and higher catalytic activity than the pure graphene sheets.