In order to reduce the negative impact on the environment caused by the massive accumulation of red mud (RM) and Yellow River sand (YRS), new alkali-excited granulated blast-furnace slag (GGBS)/RM/YRS (AGRY) geopolymer cementitious materials were prepared by combining RM and YRS with GGBS in different ratios and using sodium silicate as the alkali exciter. The effects of YRS dosage and different curing conditions on the mechanical properties, hydration products, and pore structure of cementitious materials were investigated and analyzed in terms of cost and carbon emissions. The results showed that when the dosage of YRS was 40%, the compressive strength of the prepared AGRY cementitious material could reach 48.8 MPa at 28 d under standard curing, which showed mechanical properties comparable to those of the cementitious material without YRS. The cementitious material has a more compact internal structure, and the combination of RM and YRS promotes the chemical reaction of Al and Si elements and generates the (N, C)-A-S-H gel products, which are the key to the strength enhancement of the cementitious material. In addition, the prepared cementitious material is only 90% of the cement cost for the same strength and has low carbon emission accounting for only 43% of the cement carbon emission. This study not only provides a new way for the resource utilization of RM and YRS, but also contributes an excellent new environmentally friendly material for the construction industry to achieve the goal of low carbon development.