Droplet microfluidics has become a powerful tool in precision medicine, green biotechnology, and cell therapy for single-cell analysis and selection by virtue of its ability to effectively confine cells. However, there remains a fundamental trade-off between droplet volume and sorting throughput, limiting the advantages of droplet microfluidics to small droplets (<10 pl) that are incompatible with long-term maintenance and growth of most cells. We present a sequentially addressable dielectrophoretic array (SADA) sorter to overcome this problem. The SADA sorter uses an on-chip array of electrodes activated and deactivated in a sequence synchronized to the speed and position of a passing target droplet to deliver an accumulated dielectrophoretic force and gently pull it in the direction of sorting in a high-speed flow. We use it to demonstrate large-droplet sorting with ~20-fold higher throughputs than conventional techniques and apply it to long-term single-cell analysis of Saccharomyces cerevisiae based on their growth rate.