Aneuploidy, or having a disrupted genome, is an aberration commonly found in tumours but rare in normal tissues. It gives rise to proteotoxic stress as well as a stereotypical oxidative shift, which makes these cells sensitive to internal and environmental stresses. UsingDrosophilaas a model, we investigated the changes in transcription in response to ongoing changes to ploidy (chromosomal instability, CIN). We noticed changes in genes affecting one-carbon metabolism, specifically those affecting the production and use of s-adenosyl methionine (SAM). The depletion of several of these genes has led to cell death by apoptosis in CIN cells but not in normal proliferating cells. We found that CIN cells are particularly sensitive to SAM metabolism at least partly because of its role in generating polyamines. Feeding animals spermine was seen to rescue the cell death caused by the loss of SAM synthase in CIN tissues. The loss of polyamines led to decreased rates of autophagy and sensitivity to reactive oxygen species (ROS), which we have shown to contribute significantly to cell death in CIN cells. These findings suggest that a well-tolerated metabolic intervention such as polyamine inhibition has the potential to target CIN tumours via a relatively well-characterised mechanism.