Ion-irradiation was observed to transform MgAl2O4 spinel first to a metastable crystalline phase and then to an amorphous phase at cryogenic temperatures. Elastic stiffening of 15% occurred upon formation of the metastable crystalline phase. A second transformation from the metastable crystalline spinel to an amorphous state was accompanied by elastic softening of 25% relative to unirradiated spinel. This phase transformation behavior in spinel appears to be different from that in intermetallic compounds where only elastic softening associated with radiation damage accumulation is observed. A two-stage radiation damage model is proposed to explain the observed phase transformations.