In this work, pristine, S- and P-doped monolayer graphene are studied by employing full-potential linear augmented plane-wave method within the framework of density functional theory. One and two C atom in the 2x2 supercell of monolayer graphene are replaced by S or P atoms to explore the impact of increasing doping concentration of these reactive nonmetal dopants on the electronic and optical properties. It is found that the incorporation of single S and P dopants in monolayer graphene causes the conduction band minimum at the high symmetry K-point to shift below the Fermi level along with opening the energy states at the Dirac cone; transforming the semi-metallic nature of pristine graphene to an extrinsic n-type semiconductor. Furthermore, we show that increasing the doping concentration of S and P atoms by doping them in nearest-neighbour sites in the honeycomb graphene lattice causes conduction band states to overlap with the valence band of the undoped system; allowing the re-emergence of Dirac cone. The effect of increasing S and P doping concentration on the optical properties of graphene are also studied. Our results indicate that overall absorption spectra of monolayer graphene is red shifted towards lower energy photons upon doping with P and S atoms, while refraction index, extinction coefficient and reflectivity of monolayer graphene are also significantly altered. The electron energy loss function and X-ray absorption spectroscopy results for the S- and P-doped monolayer graphene also show significant changes when compared with pristine system owing to the shifts in the pi* and sigma* anti-bonding states. Our results provide useful information for tailoring the electronic structure and optical properties of monolayer graphene through S and P doping for its applications in contemporary nano-electronic technologies.