We present a droplet-based surface acoustic wave (SAW) system designed to viably detach biological cells from a surface and sort cell types based on differences in adhesion strength (adhesion contrast) without the need to label cells with molecular markers. The system uses modulated SAW to generate pulsatile flows in the droplets and efficiently detach the cells, thereby minimizing the SAW excitation power and exposure time. As a proof of principle, the system shows efficient sorting of HEK 293 from A7r5 cells based on adhesion contrast. Results are obtained in minutes with sorting purity and efficiency reaching 97% and 95%, respectively.