During anaphase, spindle elongation pulls sister chromatids apart until each pair is fully separated. In turn, cytokinesis cleaves the cell between the separated chromosomes. What ensures that cytokinesis proceeds only after that all chromosome arms are pulled out of the cleavage plane was unknown. Here, we show that a signaling pathway, which we call NoCut, delays the completion of cytokinesis in cells with spindle-midzone defects. NoCut depends on the Aurora kinase Ipl1 and the anillin-related proteins Boi1 and Boi2, which localize to the site of cleavage in an Ipl1-dependent manner and act as abscission inhibitors. Inactivation of NoCut leads to premature abscission and chromosome breakage by the cytokinetic machinery and is lethal in cells with spindle-elongation defects. We propose that NoCut monitors clearance of chromatin from the midzone to ensure that cytokinesis completes only after all chromosomes have migrated to the poles.