Topological semimetals, especially topological semimetallic carbon-based materials, exhibit high electrical conductivity that is resistant to disruptions from defects or impurities, making them ideal alternatives as anode materials for sodium-ion batteries (SIBs). Recently, a novel two-dimensional carbon allotrope known as graphene+ was theoretically proposed [Yu et al., Cell Rep. Phys Sci., 3, 100790 (2022)], and because of its fascinating features, it shows potential for a variety of applications. In this study, we proposed two new two-dimensional carbon-based materials named M2C7 (M = B and Si) monolayers, which can be obtained by doping boron and silicon atoms into graphene+ at sp2-site, and thoroughly investigated their suitability for use as SIB anode materials. We found they exhibit distinctive mechanical and electronic properties, including negative Poisson's ratios and topological Dirac nodal-line semimetal features, along with excellent dynamic, mechanical, and thermal stability. Particularly noteworthy is that M2C7 (M = B and Si) monolayers show high energy densities for Na adsorption attributed to their elevated storage capacity (2028.65 and 1528.76 mA h g-1), lower barrier energy (0.29 and 0.14 eV), and minimal volumetric variation (1.0% and 0.27%) compared to pristine graphene+ (with values of 1487.70 mA h g-1, 0.16 eV, and 0.30%, respectively). These findings demonstrate the potential of M2C7 monolayers as high-performance SIB anode materials.