This experimental laboratory study examines the potential use of tire-derived aggregate (TDA) products as an additive to alleviate the inferior geotechnical properties of a subgrade deposit of clay soil with high expansivity. A total of ten mix designs—the unamended soil and nine soil–TDA blends prepared at 5%, 10% and 20% TDA contents (by dry mass) using three different TDA gradations/sizes—were examined. The experiments included standard Proctor compaction, oedometer swell and unconfined compression tests. The TDA materials’ lower specific gravity, hydrophobic character and higher energy absorption capacity compared with the soil solids led to notable reductions in the soil compaction characteristics. The amendment of the soil with TDA resulted in notable decreases in the rate and magnitude of swelling—the observed reductions were in favor of higher TDA contents, with larger TDA particle size being a secondary factor. Further, for any given TDA size, the variations of strength and toughness with respect to TDA content exhibited rise–fall relationships, peaking at 5% TDA and then decreasing for higher TDA contents. The stiffness and ductility parameters, however, were found to monotonically decrease and increase with the TDA content, respectively. Finally, TDA contents of up to 10%, with gradations equivalent to those of medium and coarse sands, were found to reduce the soil’s swelling potential from high to moderate expansivity, while simultaneously improving its strength-related features, and thus can be deemed as optimum mix design choices from a geotechnical perspective.