Rechargeable sodium/chlorine (Na/Cl2) batteries are emerging candidates for sustainable energy storage owing to their superior energy densities and the high abundance of Na and Cl elements. However, their practical applications have been plagued by the poor rate performance (e.g., a maximum discharge current density of 150 mA/g), as the widely used carbon nanosphere cathodes show both sluggish electron‐ion transport and reaction kinetics. Here, by mimicking the sufficient mass and energy transport in a sponge, we report a bicontinuous‐structured carbon cubosome with heteroatomic doping, which allows efficient Na‐ion and electron transport and promotes Cl2 adsorption and conversion, thus unlocking ultrahigh‐rate Na/Cl2 batteries, e.g., a maximum discharge current density of 16,000 mA/g that is more than two orders of magnitude higher than previous reports. The optimized solid–liquid–gas (carbon–electrolyte–Cl2) triple interfaces further contribute to a maximum reversible capacity and cycle life of 2,000 mAh/g and 250 cycles, respectively. Our study establishes a universal approach for improving the sluggish kinetics of conversion‐type battery reactions, and provides a new paradigm to resolve the long‐standing dilemma between high energy and power densities in energy storage devices.