The defects formed at transfer of graphene layers from a copper substrate using a PET/EVA thermoplastic were analyzed. It is shown that the damages of graphene layer occur at the stage of thermal sintering of samples and mechanical separation of copper. A method for stabilizing the copper foil and polymer substrate, which makes it possible to minimize the mechanical defects at sample separation, is proposed. The transfer process for the PET/EVA system was optimized by the sintering temperature. The PET/EVA-graphene composites with the resistance of 1.5–8 kΩ/□ were obtained using single-layer and few-layer CVD graphene at transfer.