The efficient extraction of (bio)molecules from fluid mixtures is vital for applications ranging from target characterization in (bio)chemistry to environmental analysis and biomedical diagnostics. Inspired by biological processes that seamlessly synchronize the capture, transport and release of biomolecules, we designed a robust chemomechanical sorting system capable of the concerted catch and release of target biomolecules from a solution mixture. The hybrid system is composed of target-specific, reversible binding sites attached to microscopic fins embedded in a responsive hydrogel that moves the cargo between two chemically distinct environments. To demonstrate the utility of the system, we focus on the effective separation of thrombin by synchronizing the pH-dependent binding strength of a thrombin-specific aptamer with volume changes of the pH-responsive hydrogel in a biphasic microfluidic regime, and show a non-destructive separation that has a quantitative sorting efficiency, as well as the system's stability and amenability to multiple solution recycling.