The mechanism of sulfate attack on alkali-activated materials, particularly the alkali-activated self-consolidating concrete (AASCC), is complex and contradictory. This could be due to the wide range of precursor and activator materials used in the production of AASCC mixtures, which has called into question the reliability and validity of existing evaluation procedures and practices. This paper presents a systematic research effort on AASCC mixtures, based on granulated blast-furnace slag, prone to various sulfate attack scenarios that are thought necessary to establish a proposed criterion. The conducted experimental design demonstrated that single-, binary-, and ternary-precursor AASCC samples, activated with 1:1 Na2CO3 and MetaNa2SiO3, partially submerged in sodium, magnesium, and mixed sulfate solutions could experience a dual sulfate attack scheme. Sulfate attack can occur in the immersed section in sulfate solutions, while physical sulfate attack can occur in the portion above the solution level. The influence of physical sulfate attack on the concrete’s characteristics was not significant given that the damage was confined to the outer surface. However, the damage was primarily monitored by the AASCC different systems’ pore structure, which resulted in the leaching of ions from samples to solutions. It was found that maintaining the pH in the sulfate solutions increased the rate of damage of AASCC mixtures. Furthermore, binary, and ternary precursor blends partially replacing slag with SF, or FA resulted in decreased porosity, surface scaling, and AASCC deterioration caused by an expansion in the volume of very small diameter pores. Finally, in all AASCC systems, gypsum and ettringite were the primary degradation products of sulfate attack.