Basalt rock waste is a major industrial waste generated as a result of quarrying rocks and artificial sand manufacture for construction projects, and its disposal can lead to several landfill hazards. However, it shows potential to be used as a source material for the manufacture of geopolymers. This paper presents the triaxial stress-strain characteristics of a novel geopolymer developed from basalt rock waste considering partial replacement with ground granulated blast furnace slag (GGBFS) up to 30%. A detailed mix design investigation revealed the optimum molarity (M) of the sodium hydroxide solution to be 8M and the optimum ratio (R) of sodium silicate to sodium hydroxide solution to be 0.75. The axial stress-strain relationships were developed after a series of triaxial laboratory tests for low confining pressures (0 to 800 kPa) and Hoek cell tests for high confining pressures (1 to 5 MPa). A constitutive model predicting the complete stress-strain behavior is proposed. The geopolymer stress-strain behavior shows some degree of similarity to Portland cement binder; however, differences such as an increase in stiffness and reduction in ductility were observed. Scanning electron microscopy (SEM) images also suggested a dense geopolymer gel formation resulting in a homogeneous and compact microstructure. This study demonstrates that the innovative material proposed herein produced from industrial wastes has characteristics suitable for use as an alternative and sustainable construction material.