This work presents the results of investigation of the primary minerals and their weathering products of two tailing ponds near the villages of Rudňany and Slovinky in eastern Slovakia. The tailings are near-neutral or slightly alkaline (pH = 7.2–8.8) because the acidity generated by the decomposition of the sulfides is efficiently neutralized by the abundant carbonate minerals. The most frequent primary gangue minerals are siderite, quartz, barite, and muscovite. The prevailing primary sulfide minerals in both tailing ponds are pyrite and chalcopyrite; less common are tetrahedrite and arsenopyrite. The most frequent secondary and tertiary (i.e., formed in the tailings, not in the oxidation zone of the deposits) minerals at both localities are iron oxides, either goethite or poorly crystalline hydrous ferric oxide. Other minerals (cuprite, malachite, delafossite; identified by X-ray microdiffraction or Raman spectroscopy) are minor or rare and occur only in Slovinky. The iron oxide minerals are enriched in a suite of elements, including Cu, Si, Ca, Zn, As, Mg, and Mn. The transformations of the poorly crystalline hydrous ferric oxide to goethite and maturation of goethite is controlled by both high-valence tetrahedral cations (Si, As, P) and lower-valence octahedral cations (Cu), as shown by the measurements of the size of coherently diffracting domains in goethite and the chemical composition of goethite. The iron oxide minerals, by virtue of their adsorption capacity, prevent separate minerals of many metals and metalloids (Cu, Ca, As, Sb) from nucleating and growing, and therefore control the entire neutral mine drainage (NMD) system. Geochemical modeling of the discharged waters shows that all common Cu and ferric arsenate minerals are strongly undersaturated, confirming the central role of iron oxide phases in the NMD system.