Inhibition of the spindle assembly checkpoint kinase TTK causes chromosome mis-segregation and tumor cell death. However, high levels of TTK correlate with chromosomal instability (CIN), which can lead to aneuploidy. We show that treatment of tumor cells with the selective small molecule TTK inhibitor NTRC 0066-0 overrides the mitotic checkpoint, irrespective of cell line sensitivity. In stable aneuploid cells NTRC 0066-0 induced acute CIN, whereas in cells with high levels of pre-existing CIN there was only a small additional fraction of cells mis-segregating their chromosomes. In proliferation assays stable aneuploid cells were more sensitive than cell lines with pre-existing CIN. Tetraploids are thought to be an intermediate between diploid and unstable aneuploid cells. TTK inhibitors had the same potency on post-tetraploid and parental diploid cells, which is remarkable because the post-tetraploids are more resistant to mitotic drugs. Finally, we confirm that the reference compound reversine is a TTK inhibitor and like NTRC 0066-0, inhibits the proliferation of patient-derived colorectal cancer organoids. In contrast, treatment with TTK inhibitor did not reduce the viability of non-proliferating T cell acute lymphoblastic leukemia cells samples. Consequently, TTK inhibitor therapy is expected to spare non-dividing cells, and may be used to target stable aneuploid tumors.