Colloidal particles are considered to be essential building blocks for creating innovative self-assembled and active materials, for which complexity beyond that of compositionally uniform particles is key. However, synthesizing complex, multi-material colloids remains a challenge, often resulting in heterogeneous populations that require post-synthesis purification. Leveraging advances brought forward in the purification of biological samples, here we apply fluorescence-activated cell sorting (FACS) to sort colloidal clusters synthesized through capillary assembly. Our results demonstrate the effectiveness of FACS in sorting clusters based on size, shape, and composition. Notably, we achieve a sorting purity of up to 97% for clusters composed of up to 9 particles, albeit observing a decline in purity with increasing cluster size. Additionally, dimers of different colloids can be purified to over 97%, while linear and triangular trimers can be separated with up to 88% purity. This work underscores the potential of FACS as a promising and little-used tool in colloidal science to support the development of increasingly more intricate particle-based building blocks.