Chromosomal passenger proteins have emerged as key players in the regulation of mitosis and cytokinesis. Histone deacetylase inhibitors (HDACi) are a class of anticancer drugs that induce aberrant mitosis and can overcome the spindle assembly checkpoint. Here, we investigate the mechanism by which HDACi disrupt normal mitotic progression and checkpoint function. We demonstrate that HDACi treatment temporarily delays mitotic progression through prometaphase due to activation of the spindle assembly checkpoint. Despite failing to congress chromosomes to the metaphase plate, cells aberrantly segregate their chromosomes and exit mitosis to undergo a failed cytokinesis. We show that this premature exit from mitosis is a form of mitotic slippage. Chromosomal passenger proteins fail to accumulate at the centromere following HDACi treatment. This results in inadequate concentrations of chromosomal passenger proteins at the centromere, which are insufficient to regulate the phosphorylation of the kinetochore checkpoint component BubR1, and an inability to maintain the mitotic arrest. Thus, the centromeric accumulation of chromosomal passenger complex components is critical for regulating kinetochore but not centromeric processes, and failure of this accumulation underlies the HDACi-induced mitotic slippage.