The separation of biological cells by filtration through microstructured constrictions is limited by unpredictable variations of the filter hydrodynamic resistance as cells accumulate in the microstructure. Applying a reverse flow to unclog the filter will undo the separation and reduce filter selectivity because of the reversibility of low-Reynolds number flow. We introduce a microfluidic structural ratchet mechanism to separate cells using oscillatory flow. Using model cells and microparticles, we confirmed the ability of this mechanism to sort and separate cells and particles based on size and deformability. We further demonstrate that the spatial distribution of cells after sorting is repeatable and that the separation process is irreversible. This mechanism can be applied generally to separate cells that differ based on size and deformability.