Two-dimensional porous nanosheets based on tetraoxacirculene and its analogue are theoretically studied using first principles calculations focusing on their thermal stability and mechanical, electronic, optical and thermoelectric properties. It is found that the nanosheets composed of tetraoxacirculene (TO8C) and tetraazacirculene (TA8C) are thermodynamically and kinetically stable. Both sheets show anisotropic Young's moduli corresponding to tetragonal symmetry. However, due to their porosity, the Young's moduli of both sheets are much smaller than that of graphene. Electronic structure calculations indicate that both TO8C and TA8C nanosheets are direct semiconductors with a band gap of 1.92 eV and 1.83 eV respectively, and they can adsorb strongly visible light and exhibit a huge Seebeck coefficient. Thus they can be promising candidates for solar and thermoelectric applications.