We demonstrate the growth of multilayer and single layer graphene on copper foil using bipolar pulsed direct current (DC) magnetron sputtering of a graphite target in pure Ar atmosphere. Single layer and few layer graphene films (SG and FLG) are deposited at temperatures ranging from 700-920 °C in less than 30 minutes. We find that the deposition and post-deposition annealing temperatures influence the layer thickness and quality of the graphene films formed. The films were characterized using atomic force microscopy (AFM), scanning electron microscopy (SEM), High resolution transmission electron microscopy (HRTEM), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and optical transmission spectroscopy techniques. Based on the above studies, a diffusion controlled mechanism was proposed for the graphene growth. A single step whole blood assay was used to investigate the anticoagulant activity of graphene surfaces. Platelet adhesion, activation and morphological changes on the graphene/glass surfaces compared to bare glass were analysed using fluorescence microscopy and SEM techniques. We have found significant suppression of the platelet adhesion, activation and aggregation on the graphene covered surfaces compared to the bare glass, indicating the anticoagulant activity of the deposited graphene films. Our production technique represents an industrially relevant method for the growth of single and few layer graphene for various applications including the biomedical field.