Abstract: In order to efficiently predict the mechanical properties of ternary solid waste geopolymer grouting materials (Geopolymer Grouting Material, GGM), this study conducted tests on the mechanical properties of geopolymer grouting materials with different mix ratios. The experimental design included varying amounts of three solid waste materials: slag, red mud, and fly ash. Additionally, the influence of activator concentration and curing period on the mechanical properties was investigated. A back-propagation neural network (Back propagation neural network, BPNN) model was established, and the particle swarm optimization (Particle swarm optimization, PSO) algorithm was employed to optimize the BPNN model, thereby enhancing prediction accuracy. Furthermore, the SHAP (Shapley Additive exPlanations) method was utilized for an interpretability analysis of the model’s predictions, clearly identifying the contributions of each variable to the compressive strength prediction. Correlation analysis indicates a significant positive correlation between slag content and compressive strength. Specifically, the slag content exhibits a significant positive correlation with compressive strength at different curing periods (3, 7, 28, 56 d), with correlation coefficients of 0.260, 0.215, 0.348, and 0.326, respectively. In contrast, red mud content shows a significant negative correlation with compressive strength, reaching –0.556 at the 56th day. The excessive incorporation of red mud leads to a reduction in strength. The influence of fly ash on compressive strength was relatively minor, primarily observed at longer curing periods. The activator concentration had the most significant effect on compressive strength at 28 d, with its influence surpassing that of other variables. SHAP analysis further highlighted that curing period and activator concentration were the primary positive factors affecting compressive strength. As the curing period increased, the distribution of SHAP values shifted towards the positive region, with the promoting effect on strength becoming significantly more pronounced. Higher activator concentrations corresponded to larger positive SHAP values, indicating that the activator effectively accelerates the dissolution and reaction of active components in slag and fly ash, improving the material's density and strength. However, an excessive amount of activator may lead to adverse effects. Higher levels of fly ash and slag played a lesser role, but under certain conditions, slag had a positive effect on strength through the formation of C–S–H gels. At higher red mud content, SHAP values were concentrated in the negative region, reflecting a negative contribution, as the inert components in red mud hindered the hydration reaction and reduced strength. However, at lower red mud content, SHAP values were positive, suggesting a strength-enhancing effect. On the untrained dataset, the PSO–BPNN model outperformed the traditional BPNN in prediction accuracy. Specifically, the R² value of the PSO–BPNN model improved by approximately 0.5% compared to BPNN, while the mean absolute error, mean squared error, and root mean squared error were reduced by approximately 11.8%, 21.2%, and 11.3%, respectively. The error range and frequency of extreme errors were significantly reduced, indicating that the PSO–BPNN model exhibited greater stability in handling complex data and could effectively correct systematic biases. Its strong generalization capability allows it to maintain high prediction accuracy even when confronted with unknown data, providing reliable data support for the performance prediction and mix ratio design of geopolymer grouting materials.