Many cancers are aneuploid. However, the precise role that chromosomal instability plays in the development of cancer and in the response of tumours to treatment is still hotly debated. Here, to explore this question from a theoretical standpoint we have developed an agent-based model of tissue homeostasis in which to test the likely effects of whole chromosome mis-segregation during cancer development. In stochastic simulations, chromosome mis-segregation events at cell division lead to the generation of a diverse population of aneuploid clones that over time exhibit hyperplastic growth. Significantly, the course of cancer evolution depends on genetic linkage, as the structure of chromosomes lost or gained through mis-segregation events and the level of genetic instability function in tandem to determine the trajectory of cancer evolution. As a result, simulated cancers differ in their level of genetic stability and in their growth rates. We used this system to investigate the consequences of these differences in tumour heterogeneity for anti-cancer therapies based on surgery and anti-mitotic drugs that selectively target proliferating cells. As expected, simulated treatments induce a transient delay in tumour growth, and reveal a significant difference in the efficacy of different therapy regimes in treating genetically stable and unstable tumours. These data support clinical observations in which a poor prognosis is correlated with a high level of chromosome mis-segregation. However, stochastic simulations run in parallel also exhibit a wide range of behaviours, and the response of individual simulations (equivalent to single tumours) to anti-cancer therapy prove extremely variable. The model therefore highlights the difficulties of predicting the outcome of a given anti-cancer treatment, even in cases in which it is possible to determine the genotype of the entire set of cells within the developing tumour.