In an attempt to increase sustainability of construction materials, both ground granulated blast-furnace slag (GGBS) and, less popular, copper slag (CS) can be used in alkali-activated composites. However, such composites are often more susceptible to cracking, triggered by the self-desiccation processes. The addition of superabsorbent polymers (SAP) may enable internal curing of concrete and prevent excessive cracking. Thus, this paper aims to evaluate the effectiveness of SAP as an internal curing agent for alkali-activated slag mortars containing GGBS and CS. The samples were activated by sodium silicate using 6.5% Na2O by mass of precursor. The evaluation was based on the analysis of mechanical properties, autogenous shrinkage, and water absorption capacity of two types of SAPs. Depending on the type of polymer, a higher alkali concentration in SAP solutions speeds up early age reactions up to 7 days. After this period, SAP collapses and reactions follow at the same pace as the reference sample. In the presence of CS, SAP with higher absorption and smaller particles well-distributed in the mix leads to a higher extension of reactions, observed in higher values of autogenous shrinkage (AS). This results in increased compressive strength of GGBS-CS mortars, achieving values 8.8% greater than the reference sample (without SAP) at 6 months. Although its leads to higher cracking susceptibility, SAP can improve mechanical properties and promote new applications for sustainable material containing copper slag.