To study the key factors that affect the mechanical properties of polymer materials and explore the relationship between mineral crystal formation and strength development, fly ash (FA) polymer samples were prepared using sodium hydroxide, slag, liquid sodium silicate, and hydrated lime as activators. A change in the compressive strength was observed, and X-ray diffraction measurements were carried out to confirm the change. The effects of different types and amounts of activators on the formation and transformation of mineral crystals in FA polymer samples as well as on the development of compressive strength were studied. Moreover, the relationship between the formation and transformation of mineral crystals and the development of compressive strength was established. The results show that the strongly alkaline excitation environment established by sodium hydroxide is the prerequisite for crystal formation and development of compressive strength. Under this strongly alkaline excitation environment, slag, hydrated lime, and liquid sodium silicate can increase the amounts of calcium and silicon, which promote the formation and development of hydrated calcium silicate and hydrated calcium silicoaluminate in polymers and significantly improve the compressive strength.