We demonstrate the development of an effective technique to remove the poly methyl methacrylate (PMMA) layer used for transferring graphene synthesized by a chemical vapor deposition (CVD). This was achieved utilizing electron-beam bombardment and following developing processes, prior to the use of conventional organic solvents. Field-effect transistors were fabricated on the transferred graphene in order to explore their Dirac points and carrier motilities in the ambient condition - the results were then compared with those from the conventional wet chemical treatment. It was found that the Dirac points were located close to the zero gate bias when compared to those from the acetone and the acetic acid treatments. Most significantly, the field-effect mobility reached as high as 6770 cm2/Vs and 7350 cm2/Vs on average for holes and electrons, respectively, which is more than seven times improvement in comparison to conventional acetone treatments for CVD-grown graphene devices.