As the most widely used building material, cement has attracted the attention of scholars because of its large carbon emission. To alleviate the problems of carbon emission and limited resource use caused by cement production, this study focuses on the performance of mortar after carbonization curing by regulating the composition of ternary binders. Testing involved mechanical parameters, carbon shrinkage, water absorption, hydration product, microstructure, adsorption of carbon dioxide, calcium carbonate content, and carbonization degree of mortar, as well as comparisons with the effect of calcium carbide slag and sintered red mud. We carried out several studies which demonstrated that carbonization curing and adjusting the content of calcium carbide slag and sintered red mud were beneficial to improve the mechanical properties, peak load displacement, slope, elastic energy, plastic energy, carbon shrinkage, carbon dioxide adsorption, calcium carbonate content, and carbonization degree of mortar, while the addition of calcium carbide slag and sintered red mud increased the water absorption of mortar, and the greater the dosage, the greater the water absorption. Meanwhile, adding 25%–50% calcium carbide slag and sintered red mud still had negative effects on the mechanical properties of mortar. But carbonation curing and the addition of calcium carbide slag and sintered red mud could promote the hydration reaction and consume calcium hydroxide formed by hydration to form calcium carbonate. When the dosage was 50%, the carbon dioxide adsorption capacity, calcium carbonate content, and carbonization degree of calcium carbide slag mortar were higher than those of sintered red mud mortar, which increased by 29.56%, 102.73%, and 28.84%, respectively. By comparison, calcium carbide slag and sintered red mud still showed superior carbon sequestration capacity, which was higher than fly ash and Bayer red mud. From the experiment, we came to realize that adjusting the composition of cementitious materials could realize the carbon sequestration of cement-based materials and promote the road toward low-carbon sustainable development of cement.