Geopolymer recycled aggregate concrete (GRAC) was prepared by replacing cement with geopolymer and natural aggregate with waste concrete. The effect of the water-glass module on the mechanical properties of GRAC was studied. It was found that water-glass has a double-layer structure. The low module water-glass leads to a thicker diffusion layer and more Na+ and OH− in the solution, which activates more CaO, SiO2, and Al2O3 in the raw material, and improves the strength of GRAC. Moreover, two kinds of gel structures, namely layered C-A-S-H (calcium silicate hydrate) and networked N-A-S-H (zeolite), were found in the products of geopolymer. As the water-glass module changed, the phase of zeolite changed significantly, whereas the calcium silicate hydrate did not change, indicating that the decrease in the water-glass module contributes to the formation of more N-A-S-H gel. The compressive strengths of GRAC with the sizes of 200, 150, and 100 mm3 were in line with Bazant’s size effect theoretical curve. Through the segmented fitting method, the relationship of the size conversion coefficient of GRAC (α), the critical strength (fcr), the critical dimension (Dcr), and the water-glass module (ε) were determined. It was found that ε = 1.5 is the segmented point of the three equations. The elastic modulus and peak stress of GRAC are inversely proportional to the water-glass module, and the peak strain is proportional to the water-glass module, indicating that by reducing the water-glass module, the strength of GRAC can be improved, but the brittleness is increased. The constitutive equation of GRAC with only the water-glass module as a variable was also established. It was found that the polynomial mathematical model and rational fraction mathematical model are optimal for the rising-stage and falling-stage, respectively, and the relationship between the parameters of the rising-stage (a) and the falling-stage (b), and the water-glass module, is given.