An alkali–silica reaction (ASR) is a chemical process that leads to the formation of an expansive gel, potentially causing durability issues in concrete structures. This article investigates the properties and behaviour of ASR products in mortar with the addition of low-purity calcined clay as an additional material. This study includes an evaluation of the expansion and microstructural characteristics of the mortar, as well as an analysis of the formation and behaviour of ASR products with different contents of calcined clay. Expansion tests of the mortar beam specimens were conducted according to ASTM C1567, and a detailed microscopic analysis of the reaction products was performed. Additionally, their mechanical properties were determined using nanoindentation. This study reveals that with an increasing calcined clay content, the amount of the crystalline form of the ASR gel decreases, while the nanohardness increases. The Young’s modulus of the amorphous ASR products ranged from 5 to 12 GPa, while the nanohardness ranged from 0.41 to 0.67 GPa. The obtained results contribute to a better understanding of how the incorporation of low-purity calcined clay influences the ASR in mortar, providing valuable insights into developing sustainable and durable building materials for the construction industry.