Ground granulated blast furnace slag (GGBFS) is broadly utilized as a mineral admixture in concrete production. This study shows a procedure for the optimal design of a sustainable concrete mix with GGBFS considering carbonation coupled with stress. First, the objective of optimal design is positioned as the total cost of materials and CO2 emissions. The proposed procedure covers different constraints, such as strength, slump, and carbonation durability with sustained stress. Second, a genetic algorithm is used to find the optimal mixtures considering the objective function and various constraints. This analysis results show the following: (1) For low-strength concrete, carbonation is a critical factor and can dominate the mixture of sustainable concrete. Moreover, stress levels and types affect the carbonation and optimal mixture. A rich mixture is essential for structural elements with high-level stress. In contrast to compressive stress, the influence of tensile stress on mixtures is much more apparent. (2) For strong concrete, carbonation depth is less than cover depth and is not a dominant constraint in designing the mixture, and strength is the dominant factor in designing high-strength concrete. In summary, the suggested model is a general way to design mixtures considering strength, slump, carbonation durability with sustained stress.