We report a novel pressure-driven spin crossover in layered cobalt oxyfluoride Sr2CoO3F with a distorted CoO5 square pyramid loosely bound with a fluoride ion. Upon increasing pressure, the spin state of the Co(III) cation gradually changes from a high spin state (S = 2) to a low spin state (S = 0) accompanied by a anomalously large volume contraction (bulk modulus, 76.8(5) GPa). The spin state change occurs on the CoO5 pyramid in a wide pressure range, but the concomitant gradual shrinkage of the Co-F bond length with pressure gives rise to a polyhedral transformation to the CoO5F octahedron without a structural phase transition, leading to the full conversion to the LS state at 12 GPa. The present results provide new effective strategy to fine-tune electronic properties of mixed anion systems by controlling the covalency in metal-ligand bonds under pressure.