Microtubule-targeting cancer drugs such as paclitaxel block cell-cycle progression at mitosis by prolonged activation of the mitotic checkpoint. Cells can spontaneously escape mitotic arrest and enter interphase without chromosome segregation by a process termed mitotic slippage that involves the degradation of cyclin B1 without mitotic checkpoint inactivation. Inducing mitotic slippage with chemicals causes cells to die after multiple rounds of DNA replication without cell division, which may enhance the antitumor activity of microtubule-targeting drugs. Here, we explore pathways leading to mitotic slippage by using SU6656 and geraldol, two recently identified chemical inducers of mitotic slippage. Mitotic slippage induced by SU6656 or geraldol was blocked by the proteasome inhibitor MG-132 and involved proteasome-dependent degradation of cyclin B1 and the mitotic checkpoint proteins budding uninhibited by benzimidazole related 1 (BubR1) and cell division cycle 20 (Cdc20) in T98G cells. Mitotic slippage and the degradation of BubR1 and Cdc20 were also inhibited by the caspase-3 and -7 inhibitor DEVD-CHO. MCF-7 cells lacking caspase-3 expression could not degrade BubR1 or undergo mitotic slippage in response to SU6656 or geraldol. Introduction of caspase-3 completely restored the ability of MCF-7 cells to degrade BubR1 and undergo mitotic slippage. However, lack of expression of caspase-3 did not affect cell death after exposure to paclitaxel, with or without mitotic slippage induction. The requirement for caspase-3 for chemically induced mitotic slippage reveals a new mechanism for mitotic exit and a link between mitosis and apoptosis that has implications for the outcome of cancer chemotherapy.