Based on the molecular dynamics simulations, mechanical properties of the most recently synthesized covalent fullerene network, i.e., graphullerene sheet, under uniaxial tension, are determined. These properties include Young's modulus, ultimate stress, failure strain, tensile toughness, and Poisson's ratio. Due to the lack of existing data on mechanical properties of graphullerene, a comprehensive study is performed to get an insight into the effects of defect density, size, and temperature on all tensile characteristics. In the results, it is indicated that the tensile behavior of graphullerene structure is comparable with graphene allotropes. Moreover, it is observed that the presence of defect reduces stiffness, ultimate stress, and tensile toughness, while it has a negligible effect on the failure strain. It is further observed that unlike stiffness, increasing the temperature reduces other tensile characteristics. Interestingly, it is found that graphullerene exhibits auxetic behavior with negative Poisson's ratio which categorizes it as a unique auxetic material ever synthesized. At the end, three types of potential functions for hydrocarbons including adaptive intermolecular reactive empirical bond order, reactive empirical bond order, and Tersoff are considered to study the tensile behavior of graphullerene. This new auxetic nanosheet is a promising analogous to the existing 2D nanostructures with fascinating potential applications.