Carbon micro/nanolattice materials, defined as three dimensional (3D) architected metamaterials made of micro/nanoscale carbon constituents, have demonstrated exceptional mechanical properties, including ultrahigh specific strength, stiffness and extensive deformability through experiments and simulations. The ductility of these carbon micro/nanolattices is also important for robust performance. In this work, we present a novel design of using reversible snap-through instability to engineer energy dissipation in 3D graphene nanolattices. Inspired by the shell structure in flexible straws, we construct its graphene counterpart via topological design and demonstrate its snap-through instability through molecular dynamics (MD). One-dimensional (1D) straw-like carbon nanotube (SCNT) and 3D graphene nanolattices are constructed using the unit cell. These graphene nanolattices possess multiple stable states and are elastically reconfigurable. A theoretical model of 1D bi-stable element chain is adopted to understand the collective deformation behavior of the nanolattice. Reversible pseudo plastic behavior with a finite hysteresis loop is predicted and further validated via MD. Enhanced by these novel energy dissipation mechanisms, the 3D graphene nanolattice shows good tolerance to crack-like flaw and is predicted to approach a specific energy dissipation of 233 kJ/kg in a loading cycle with no permanent damage (one order higher than the energy absorbed by carbon steel at failure, 16 kJ/kg). This study provides a novel mechanism for 3D carbon nanolattice to dissipate energy with no accumulative damage and improve resistance to fracture, broadening the promising application of 3D carbon in energy absorption and programmable materials.