Superatomic crystals are a class of hierarchical materials composed of atomically precise clusters assembled via van der Waals or covalent-like interactions. Au6Te12Se8, an all-inorganic superatomic superconductor exhibiting superatomic-charge-density-wave (S-CDW), provides the first platform to study the response of its collective quantum phenomenon to the external pressure in superatomic crystals. We reveal a competition between S-CDW and superconductivity in an ultra-narrow pressure range. Distinct from conventional CDW ordering, S-CDW shows the lowest threshold (0.1 GPa) toward external pressure that is 1-2 orders of magnitude lower than other atomic compounds. Prominently, a second superconducting phase emerges above 7.3 GPa with a threefold enhancement in the transition temperature (Tc) to 8.5 K, indicating a switch of the conduction channel from the a- to b-axis. In situ synchrotron diffractions and theoretical calculations reveal a pressure-mediated mesoscopic slip of the superatoms and a 2D-3D transition of the Fermi surface topology, which well explains the observed dimensional crossover of conductivity and re-entrant superconductivity.