Whole-genome doubling (WGD) is a common feature of human cancers and is linked to tumour progression, drug resistance, and metastasis1,2,3,4,5,6. Here we examine the impact of WGD on somatic evolution and immune evasion at single-cell resolution in patient tumours. Using single-cell whole-genome sequencing, we analysed 70 high-grade serous ovarian cancer samples from 41 patients (30,260 tumour genomes) and observed near-ubiquitous evidence that WGD is an ongoing mutational process. WGD was associated with increased cell–cell diversity and higher rates of chromosomal missegregation and consequent micronucleation. We developed a mutation-based WGD timing method called doubleTime to delineate specific modes by which WGD can drive tumour evolution, including early fixation followed by considerable diversification, multiple parallel WGD events on a pre-existing background of copy-number diversity, and evolutionarily late WGD in small clones and individual cells. Furthermore, using matched single-cell RNA sequencing and high-resolution immunofluorescence microscopy, we found that inflammatory signalling and cGAS-STING pathway activation result from ongoing chromosomal instability, but this is restricted to predominantly diploid tumours (WGD-low). By contrast, predominantly WGD tumours (WGD-high), despite increased missegregation, exhibited cell-cycle dysregulation, STING1 repression, and immunosuppressive phenotypic states. Together, these findings establish WGD as an ongoing mutational process that promotes evolvability and dysregulated immunity in high-grade serous ovarian cancer.