Graphene grown by chemical vapor deposition and supported on SiO2 and sapphire substrates was studied following controlled introduction of defects induced by 35 keV carbon ion irradiation. Changes in Raman spectra following fluences ranging from 1012 cm-2 to 1015 cm-2 indicate that the structure of graphene evolves from a highly-ordered layer, to a patchwork of disordered domains, to an essentially amorphous film. These structural changes result in a dramatic decrease in the Hall mobility by orders of magnitude while, remarkably, the Hall concentration remains almost unchanged, suggesting that the Fermi level is pinned at a hole concentration near 1x1013 cm-2. A model for scattering by resonant scatterers is in good agreement with mobility measurements up to an ion fluence of 1x1014 cm-2.