Cytokinesis is monitored by a molecular machinery that promotes the degradation of the intercellular bridge, a transient protein structure connecting the two daughter cells. Here, we found that CSA and CSB, primarily defined as DNA repair factors, are located at the midbody, a transient structure in the middle of the intercellular bridge, where they recruit CUL4 and MDM2 ubiquitin ligases and the proteasome. As a part of this molecular machinery, CSA and CSB contribute to the ubiquitination and the degradation of proteins such as PRC1, the Protein Regulator of Cytokinesis, to ensure the correct separation of the two daughter cells. Defects in CSA or CSB result in perturbation of the abscission leading to the formation of long intercellular bridges and multinucleated cells, which might explain part of the Cockayne syndrome phenotypes. Our results enlighten the role played by CSA and CSB as part of a ubiquitin/proteasome degradation process involved in transcription, DNA repair, and cell division.