• Cu(II) species (CuO, CuCl2, CuS) differentially affect the compressive strength and hydration of blast furnace slag–cement composites, with effects varying by grinding method and curing age.
• At 3 days, CuO and CuS enhance strength of dry-ground composites but suppress wet-ground ones; at 28 days, the trend reverses, with all three species improving wet-ground composite strength.
• CuCl2 reduces hydration degree in dry-ground composites but increases it in wet-ground ones; CuO promotes hydration in both, while CuS inhibits it.
• Immobilization efficiency depends on composite type: dry-ground composites better immobilize CuCl2, while wet-ground composites better immobilize CuO and CuS due to finer particles and denser matrix.