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We investigate the extent to which global mean temperature, precipitation, and the carbon cycle are constrained by cumulative carbon emissions throughout four experiments with a fully coupled climate–carbon cycle model. The paired experiments adopt contrasting, idealised approaches to climate change mitigation at different action points this century, with total emissions rising to more than two trillion tonnes of carbon (TtC). For each pair, the contrasting mitigation approaches—capping emissions early versus reducing them to zero a few decades later—cause their cumulative emissions trajectories to diverge initially, then converge, cross, and diverge again. We find that global mean temperature is linear with cumulative emissions across all experiments, although differences of up to 1.5 K exist regionally when the trajectories of total carbon emitted during the course of the two scenarios coincide, for both pairs of experiments. Interestingly, although the oceanic precipitation response scales with cumulative emissions, the global precipitation response does not, due to a decrease in precipitation over land above emissions of around one TtC. Most carbon fluxes are less well constrained by cumulative emissions as they reach two trillion tonnes. The opposing mitigation approaches have different consequences for the Amazon rainforest, which affects the linearity with which the carbon cycle responds to cumulative emissions. The average Transient Climate Response to cumulative carbon Emissions (TCRE) is 1.95 K TtC⁻¹, at the upper end of the Intergovernmental Panel on Climate Change's range of 0.8–2.5 K TtC⁻¹.