Dicentric chromosomes are unstable products of erroneous DNA repair events that can lead to further genome rearrangements and extended gene copy number variations. During mitosis, they form anaphase bridges, resulting in chromosome breakage by an unknown mechanism. In budding yeast, dicentrics generated by telomere fusion break at the fusion, a process that restores the parental karyotype and protects cells from rare accidental telomere fusion. Here, we observed that dicentrics lacking telomere fusion preferentially break within a 25- to 30-kb-long region next to the centromeres. In all cases, dicentric breakage requires anaphase exit, ruling out stretching by the elongated mitotic spindle as the cause of breakage. Instead, breakage requires cytokinesis. In the presence of dicentrics, the cytokinetic septa pinch the nucleus, suggesting that dicentrics are severed after actomyosin ring contraction. At this time, centromeres and spindle pole bodies relocate to the bud neck, explaining how cytokinesis can sever dicentrics near centromeres.