The single-factor experiments are designed to quantitatively investigate the effects of silica fume, mineral powder, and fly ash on the mechanical and thermal insulation properties of desulfurization gypsum-based composites (DGCs). The effect mechanism is discussed from the microscopic morphology of the internal structure, and the corresponding relationship between the strength and thermal conductivity of this material is evaluated by the regression model. The results show that the admixture of silica fume, mineral powder, and fly ash improves the strengths and thermal insulation properties of DGCs, with the order of influence silica fume > mineral powder > fly ash. The optimal 28 d compressive strength and thermal conductivity are 34.17 MPa and 0.2146 W/(m·K), respectively, at a silica fume dosage of 35%. The enhancement effects on the strength and thermal insulation performance of DGCs are attributed to the increase in the hydration products C-S-H gel and Aft. Moreover, the thermal conductivity linearly decreases with the increase in the compressive strength of DGC after adding silica fume, mineral powder, and fly ash. The linear regression models exhibit good precision for evaluating the corresponding relationships between the compressive strength and thermal conductivity of DGCs with different admixtures.