Poly(methyl methacrylate) (PMMA) is widely used for graphene transfer and device fabrication. However, it inevitably leaves a thin layer of polymer residues after acetone rinsing and leads to dramatic degradation of device performance. How to eliminate contamination and restore clean surfaces of graphene is still highly demanded. In this paper, we present a reliable and position-controllable method to remove the polymer residues on graphene films by laser exposure. Under proper laser conditions, PMMA residues can be substantially reduced without introducing defects to the underlying graphene. Furthermore, by applying this laser cleaning technique to the channel and contacts of graphene field-effect transistors (GFETs), higher carrier mobility as well as lower contact resistance can be realized. This work opens a way for probing intrinsic properties of contaminant-free graphene and fabricating high-performance GFETs with both clean channel and intimate graphene/metal contact.