The adsorption of toxic heavy metals (THMs), including cadmium (Cd), mercury (Hg), and lead (Pb), on the graphene (G) and six sulfur- and nitrogen/sulfur-co-doped graphene surfaces (G@1N@1S, G@1N@2S, G@2N@1S, G@1S, G@2S, G@3S) has been studied using electronic structure methods. The doping of graphene surface with the nitrogen and sulfur atoms increases the adsorption energies of THMs. The strongest interaction is seen with adsorption of Pb atom on the surfaces, following the order Pb>Cd>Hg and is confirmed by the atoms in molecules analysis, noncovalent interaction plots, and frontier molecular orbitals. The free energy of adsorption calculation shows that the adsorption process of Pb atoms on the surfaces is exothermic and proceeds spontaneously, while the nature of adsorption of Cd and Hg atoms is endothermic. Significant changes in the electronic structure of the surfaces are seen with adsorption of THMs. A significant change in the HOMO-LUMO energy gap (E-g) and electrical conductivity (sigma) of the surfaces is observed with adsorption of Pb atoms, in contrast to Cd and Hg atoms counterparts. Moreover, the calculated optical properties of the surfaces and their complexes with THMs using time-dependent density functional theory reveal that the absorption spectra of the surfaces undergo appreciable changes after adsorption of THMs. These studies indicate the potential use of defect engineering and decoration of vacant sites by chalcogens/pnictogens for sensing of toxic heavy metals.