Basalt-based glass materials and composite variants were synthesized from basalt rock originating from the Vrelo deposit in Serbia using the melt-quenching method. In addition to the reference basalt glass, samples containing 5 wt.% iron mine tailings originating from flotation waste in the Bor mining district, Serbia, and commercially available AISI 304 stainless steel wire mesh were prepared to investigate the effects of secondary raw materials, reinforcement, and reinforcement orientation on thermal and mechanical behavior. The materials were characterized by energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), differential thermal analysis (DTA), differential scanning calorimetry (DSC), dilatometry, compressive strength testing, and stereomicroscopy. XRD confirmed the predominantly amorphous character of the synthesized glasses. DTA and DSC revealed broad intermediate-temperature thermal responses and a reproducible thermal event near 700 °C, while dilatometry demonstrated distinct differences in the high-temperature dimensional behavior of the investigated compositions. Compressive strength was strongly influenced by composition and steel mesh orientation, with the highest value of 258.6 MPa obtained for the composite containing 5 wt.% mine tailings and steel wire mesh. Stereomicroscopy revealed differences in crack propagation, fracture morphology, and fragment retention associated with mine tailings and steel reinforcement. These results demonstrate the potential of mine-tailings-modified and steel-reinforced basalt glasses as sustainable materials with tunable thermomechanical performance.