We present a new approach to remove monolayer graphene transferred on top of a silicon-on-insulator (SOI) photonic integrated chip. Femtosecond laser ablation is used for the first time to remove graphene from SOI waveguides, whereas oxygen plasma etching through a metal mask is employed to peel off graphene from the grating couplers attached to the waveguides. We show by means of Raman spectroscopy and atomic force microscopy that the removal of graphene is successful with minimal damage to the underlying SOI waveguides. Finally, we employ both removal techniques to measure the contribution of graphene to the loss of grating-coupled graphene-covered SOI waveguides using the cut-back method.