The aluminum Bayer production process is widespread all over the world. One of the waste products of the Bayer process is a basic aluminosilicate bauxite residue called red mud. The aluminosilicate nature of red mud makes it suitable as a precursor for alkali-activated materials. In this work, red mud was mixed with different percentages of blast furnace slag and then activated by sodium silicate solution at different SiO2/Na2O ratios. Obtained samples were characterized by chemical–physical analyses and compressive strength determination. Very high values of compressive strength, up to 50 MPa, even for high percentage of red mud in the raw mixture (70 wt.% of RM in powder mixture), were obtained. In particular, the higher compressive strength was measured for cubic samples containing 50 wt.% of RM, which showed a value above 70 MPa. The obtained mixtures were characterized by no or scarce environmental impact and could be used in the construction industry as an alternative to cementitious and ceramic materials.