Using molecular dynamic simulations, the performance of carbon nitride (C2N) was studied for the separation of Cu2+ and Hg2+ as heavy metal ions from water. The high porosity of the single layer C2N nanosheet in comparison with other similar carbon-based membranes and the existence of nitrogen atoms at the edge of the pores increase the efficiency of C2N for water purification. The separation of heavy metal ions through the nanosheet is performed by applying an external voltage across the membrane. Investigation of the ions permeation through the membrane demonstrates that the permeability of the Cu2+ ions through the C2N is about 2.5 times higher than that of Hg2+. The results of radial pair distribution function analysis illustrate that the energy barrier for ions passage is due to the hydration shell of the cations. Also, the density of the cations and water molecules, and the hydrogen bonds between water molecules in the whole system are analysed for the study of the performance of C2N nanosheet for ion separation and these results demonstrate that this membrane has the selectivity performance for heavy metal removal and higher permeability of the cations than that of other carbon-based membrane because of high porosity.