Mine tailings (MT) could represent a step forward in terms of the quality of the aggregates usually used in civil engineering applications, mostly due to its high density. The Portuguese Neves Corvo copper mine, owned by the Lundin Mining Corporation, produces approximately 3 million tonnes per year. Nevertheless, it cannot be used in its original state, due to its high levels of sulphur and other metals (As, Cr, Cu, Pb, Zn). This paper focuses on the stabilisation/solidification of high-sulphur MT, without any previous thermal treatment, using alkali-activated fly ash (FA). The variables considered were the MT/FA ratio and the activator type and concentration. A fine aggregate was then added to the pastes to assess the quality of the resulting mortar. Maximum compressive strengths of 14 MPa and 24 MPa were obtained for the pastes and mortars, respectively, after curing for 24 h at 85 °C. Thermogravimetric analysis, scanning electron microscopy, X-ray energy dispersive spectroscopy, X-ray diffraction, and infrared spectroscopy were used to characterize the reaction products, and two types of leaching tests were performed to assess the environmental performance. The results showed that the strength increase is related with the formation of a N-A-S-H gel, although sodium sulphate carbonate was also developed, suggesting that the total sodium intake could be optimized without strength loss. The solubility of the analysed metals in the paste with 78% MT and 22% FA was below the threshold for non-hazardous waste.