Nutrition exerts considerable effects on health, and dietary interventions are commonly used to treat diseases of metabolic aetiology. Although cancer has a substantial metabolic component1, the principles that define whether nutrition may be used to influence outcomes of cancer are unclear2. Nevertheless, it is established that targeting metabolic pathways with pharmacological agents or radiation can sometimes lead to controlled therapeutic outcomes. By contrast, whether specific dietary interventions can influence the metabolic pathways that are targeted in standard cancer therapies is not known. Here we show that dietary restriction of the essential amino acid methionine—the reduction of which has anti-ageing and anti-obesogenic properties—influences cancer outcome, through controlled and reproducible changes to one-carbon metabolism. This pathway metabolizes methionine and is the target of a variety of cancer interventions that involve chemotherapy and radiation. Methionine restriction produced therapeutic responses in two patient-derived xenograft models of chemotherapy-resistant RAS-driven colorectal cancer, and in a mouse model of autochthonous soft-tissue sarcoma driven by a G12D mutation in KRAS and knockout of p53 (KrasG12D/+;Trp53−/−) that is resistant to radiation. Metabolomics revealed that the therapeutic mechanisms operate via tumour-cell-autonomous effects on flux through one-carbon metabolism that affects redox and nucleotide metabolism—and thus interact with the antimetabolite or radiation intervention. In a controlled and tolerated feeding study in humans, methionine restriction resulted in effects on systemic metabolism that were similar to those obtained in mice. These findings provide evidence that a targeted dietary manipulation can specifically affect tumour-cell metabolism to mediate broad aspects of cancer outcome.