Many coastal and island communities depend on groundwater as the only source of freshwater, making it an invaluable resource. In the Mediterranean region, groundwater resources are highly vulnerable to natural and anthropogenic pressures, such as overexploitation, climate change, seasonal variations in precipitation, and seawater intrusion. Hence, an understanding of hydrogeological processes and groundwater chemistry is a basis for the sustainable management of coastal and island groundwater resources. Vis, a small and remote karst island in the Adriatic Sea, exhibits peculiar geological and hydrogeological settings, resulting in the island’s autonomous water supply. The current pumping capacity (maximum of 42 l/s) meets most of the demand, but intensive summer tourism and climate change exert high stress on groundwater resources during the dry season. Consequently, in the last decade, occasional reductions for consumers occurred. Monitoring of in situ physicochemical parameters and groundwater sampling for chemical and isotopic analyses were conducted from 2020 to 2023 at deep borewells, shallow dug wells, and springs. Hydrochemical interpretation indicated that groundwater chemistry was affected primarily by carbonate and sulfate rock dissolution, mixing with seawater, reverse ion exchange, and dedolomitization. The majority of groundwater samples exhibit Ca–HCO3 hydrochemical facies, followed by Na–Cl and mixed facies. The low percentage of seawater in the mixture indicated that seawater intrusion is not too extensive even during prolonged dry periods, implying a favorable hydrostatic regime with relatively small but sufficient groundwater reserves of the island’s aquifers, although the investigated period was characterized by significantly lower precipitation with respect to the 30-year average.