The common phenomenon observed for concrete in aggressive water is leaching, which involves the dissolution of cement hydration products. Many studies have focused on leaching in demineralised water or acid attacks, but mineral water still deserves further investigation. In most standards, the aggressiveness of a given water body is determined by its pH and not its composition. The effect of the calcium content of the water on degradation is yet to be determined. In this paper, the leaching of Portland cement-based mortar was induced by two types of drinking water with different calcium contents and buffer capacity in controlled conditions. The Langelier saturation index (LSI) was used to describe water aggressiveness based on the calco-carbonic equilibrium. The studied waters had the same pH but LSIs of +0.5 and −1.0 corresponding to scaling with respect to aggressive water; demineralised water was used as a reference. Microstructural damage was checked by TGA and X-ray microtomography. Macroscopic measurements were used to monitor global degradation. The soft water caused a 53% deeper deterioration of the mortar sample than the hard water. Soft water-induced leaching was found to be similar yet slower to leaching via demineralised water (with a mass loss of −2.01% and −2.16% after 200 days, respectively). In contrast, hard water induced strongly time-dependent leaching, and the damage was located close to the surface. The roughness of leached specimens was 18% higher in hard water than in soft water. The formation of calcite on the sample surface not only affects the leaching rate by creating a protective surface layer, but it could also act as a calcium ion pump.