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High-volume slag (HVS) can reduce the CO2 emissions of concrete, but increase the carbonation depth of concrete. In particular, because of the effects of climate change, carbonation will accelerate. However, the uptake of CO2 as a result of carbonation can mitigate the harm of CO2 emissions. This study proposes an optimal mixture design method of low-CO2 HVS concrete considering climate change, carbonation, and CO2 uptake. Firstly, net CO2 emissions are calculated by subtracting the CO2 emitted by the material from the uptake of CO2 by carbonation. The strength and depth of carbonation are evaluated by a comprehensive model based on hydration. Secondly, a genetic algorithm (GA) is used to find the optimal mixture. The objective function of the GA is net CO2 emissions. The constraints of the GA include the strength, carbonation, workability, and range of concrete components. Thirdly, the results show that carbonation durability is a control factor of the mixture design of low-strength HVS concrete, while strength is a control factor of the mixture design of high-strength HVS concrete. After considering climate change, the threshold of strength control increases. With the increase of strength, the net CO2 emissions increase, while the CO2 uptake ratio decreases.