Certain copy number alterations (CNAs) are strongly associated with particular cancer types. However, the mechanisms underlying the selection of specific CNAs remain unknown. Here, we identified functional relationships between recurrent CNAs in colorectal cancers (CRCs) and adenomatous polyposis coli (APC) mutations. Quantitative phenotyping of mitotic spindles highlighted APC functions at centrosomes where APC positively regulated Aurora A kinase (AURKA). Upon APC inactivation, elevated β-catenin levels blocked AURKA activation, which caused chromosome instability and supressed proliferation, resulting in the generation and selection of AURKA-activating CNAs. Arm-level amplification of chromosomes containing AURKA and AURKA activator genes was observed in APC mutant CRCs, early stage mouse tumours, and cells in culture, which was concomitant with an increase in growth potential. Our findings demonstrate a mechanism that restores tumour cell fitness through compensatory chromosome alterations to overcome adverse effects of prior mutations, which may affect the course of cancer type-specific CNA formation.