There is a critical need for sorting complex materials, such as pancreatic islets of Langerhans, exocrine acinar tissues, and embryoid bodies. These materials are cell clusters, which have highly heterogeneous physical properties (such as size, shape, morphology, and deformability). Selecting such materials on the basis of specific properties can improve clinical outcomes and help advance biomedical research. In this work, we focused on sorting one such complex material, human stem cell-derived β cell clusters (SC-β cell clusters), by size. For this purpose, we developed a microfluidic device in which an image detection system was coupled to an actuation mechanism based on traveling surface acoustic waves (TSAWs). SC-β cell clusters of varying size (∼100-500 μm in diameter) were passed through the sorting device. Inside the device, the size of each cluster was estimated from their bright-field images. After size identification, larger clusters, relative to the cutoff size for separation, were selectively actuated using TSAW pulses. As a result of this selective actuation, smaller and larger clusters exited the device from different outlets. At the current sample dilutions, the experimental sorting efficiency ranged between 78% and 90% for a separation cutoff size of 250 μm, yielding sorting throughputs of up to 0.2 SC-β cell clusters/s using our proof-of-concept design. The biocompatibility of this sorting technique was also established, as no difference in SC-β cell cluster viability due to TSAW pulse usage was found. We conclude the proof-of-concept sorting work by discussing a few ways to optimize sorting of SC-β cell clusters for potentially higher sorting efficiency and throughput. This sorting technique can potentially help in achieving a better distribution of islets for clinical islet transplantation (a potential cure for type 1 diabetes). Additionally, the use of this technique for sorting islets can help in characterizing islet biophysical properties by size and selecting suitable islets for improved islet cryopreservation.