A combination of carbon nanotubes (CNT) and graphene in the form of macroscopic hybrid buckypaper (HBP), exhibits a unique set of properties that can be exploited for many emerging applications. Here, we present a simple, inexpensive and scalable approach for the synthesis of highly conductive auxetic graphene/CNT HBP via wet-filtration-zipping and demonstrate the electrical, electrochemical and mechanical performance (tensile, mode I and mode III fracture) of synthesized HBP. An overall increase in electrical conductivity of 247% is observed for HBP (50 wt.% graphene and 50 wt.% CNT) as compared to BP (100 wt.% CNT) due to effective electronic percolation through the graphene and CNT. As a negative electrode for lithium-ion batteries, HBP shows 50% higher gravimetric specific capacity and 89% lower charge transfer resistance relative to BP. The graphene content in the HBP influences the mechanical performance providing an auxetic structure to HBP with large negative Poisson's ratio. The facile green-chemistry approach reported here can be readily applied to any other 1D and 2D materials and solves key challenges associated with existing buckypaper manufacturing methods. The potential of the synthesis method to integrate with current cellulose paper manufacturing technology and its scalability demonstrate the novelty of the work for industrial scale production.