Red mud is a by-product of alumina production from bauxite ore by the Bayer method, which contains considerable amounts of valuable components such as iron, aluminum, titanium, and scandium. In this study, an approach was applied to extract iron, i.e., carbothermic reduction roasting of red mud with sodium and potassium carbonates followed by magnetic separation. The thermodynamic analysis of iron and iron-free components’ behavior during carbothermic reduction was carried out by HSC Chemistry 9.98 (Outotec, Pori, Finland) and FactSage 7.1 (Thermfact, Montreal, Canada; GTT-Technologies, Herzogenrath, Germany) software. The effects of the alkaline carbonates’ addition, as well as duration and temperature of roasting on the iron metallization degree, iron grains’ size, and magnetic separation process were investigated experimentally. The best conditions for the reduction roasting were found to be as follows: 22.01% of K2CO3 addition, 1250 °C, and 180 min of duration. As a generalization of the obtained data, the mechanism of alkaline carbonates’ influence on iron grain growth was proposed.