The unconfined compressive strength (qu) weakness of low-compressibility clay (CL) reduces its structural safety. As part of the present study, waste glass powder (WGP) was mixed with Portland cement to improve the geotechnical properties of clayey soil, thus contributing to sustainability through the recycling of municipal waste. Based on the stiffness and chemical composite of WGP and cement, the adopted mixing ratio of the mixed soil was 10% and 20% WGP and 3% and 6% cement. The soil mixing ratio was selected and tested considering the percentage of the cement, WGP, water/cement ratio, dry unit weight, porosity of the specimen, and curing times of 7 days and 28 days. SEM-EDS tests were conducted to examine the impact of raw materials on the microstructural mixed soil. The results from SEM-EDS show that the cement–WGP–CL mixture caused different degrees of cementation and bonding products. Modifying multiple layers of water in the particle of the clay surface led to the enhancement of the interaction of the interlayer of hydrated clay, achieving the best unconfined compressive strength and stiffness of the designed specimen. From the viewpoint of unconfined compressive strength and stiffness enhancement, blending content of 20% WGP and 6% cement and dry unit weights compaction was recommended for stabilizing CL. The process of qu and stiffness improving CL involved an optimized mixing ratio and particle densification reaction efficiency. The soil’s qu and stiffness were predicted using ANN (artificial neural networks) and the porosity/cement index was predicted based on the experimental results.