Experimentally fabricated two-dimensional (2D) carbon-based nanomaterials have received significant attention because of their ultra-high physical properties, in recent years. In this manuscript, the thermal conductivity (TC) and mechanical response of 2D B3C3 and C3N3 structures are studied in detail, using molecular dynamics (MD) simulations. Their superior mechanical properties (Young’s modulus, ultimate tensile strength and failure strain) and TC make an excellent candidate for various applications of nanodevices. The mechanical properties of these 2D structures are also examined at five various temperatures up to 900 K along with the different loading directions and various strain rates from 107 to 109 s−1. MD results demonstrate that the mechanical properties of these 2D structures gradually decrease as temperature increases, due to the weakening effect of high temprerature. Additionally, when the strain rate increases, it is revealed that the mechanical properties show an increasing trend. Furthermore, at 300 K, the failure processes of these 2D structures are studied. MD simulations results demonstrate that these structures show brittle failure mechanism. On the other hand, various types of structural defects occurs during the production process and so these defects affect the physical properties of these structures adversely. Accordingly, the effects of various atom types, such as, N, B and C, vacancy defects on the mechanical properties and TC of these structures were investigated. The existence of vacancy defects in these structures reduces the TC and mechanical properties significantly by increasing the concentrations of defects. Finally, non-equilibrium MD simulations results indicate exceptionally high TC values of these structures.