Graphene growth on a copper surface via metal-catalyzed chemical vapor deposition has several advantages in terms of providing high-quality graphene with the potential for scale-up, but the product is usually inhomogeneous due to the inability to control the graphene layer growth. The non-uniform regions strongly affect the reliability of the graphene in practical electronic applications. Herein, we report a novel graphene transfer method that allows for the selective exfoliation of single-layer graphene from non-uniform graphene grown on a Cu foil. Differences in the interlayer bonding energy are exploited to mechanically separate only the top single-layer graphene and transfer this to an arbitrary substrate. The dry-transferred single-layer grapheme showed electrical characteristics that were more uniform than those of graphene transferred using conventional wet-etching transfer steps.