Effective therapeutics exploit common characteristics shared amongst cancers. As many cancers present chromosomal instability (CIN), one possible approach to treat these cancers could be to increase their CIN above a threshold that would affect their viability. Here, we investigated whether causing polyploidy by cytokinesis failure could represent a useful approach. We show that cytokinesis failure caused by depletion of Citron kinase (CIT-K) dramatically decreased cell proliferation in breast, cervical and colorectal cancer cells. CIT-K depletion activated the Hippo tumor suppressor pathway in normal, but not in cancer cells, indicating that cancer cells have evolved mechanisms to bypass this control. CIT-K depleted cancer cells died via apoptosis in a caspase 7 dependent manner and, consistent with this, p53-deficient HCT116 colon carcinoma cells failed to induce apoptosis after cytokinesis failure. However, other p53-mutated cancer cells were able to initiate apoptosis, indicating that cytokinesis failure can trigger apoptosis through a p53-independent mechanism. Finally, we found that actively dividing and, in some cases, polyploid cancer cells were more susceptible to CIT-K depletion. In sum, our findings indicate that inducing cytokinesis failure could be a promising anti-cancer therapeutic approach for a wide range of cancers, especially those characterized by fast cell proliferation and polyploidy.