The objective of the work was to investigate and estimate the effects of conventional, organic, and biodynamic farming systems on biological and agrochemical soil properties and mineral composition of potato tubers with different colored flesh. This study compared the same biological and agrochemical soil quality indicators on samples collected at three sampling times: before potato planting, the middle of the potato season, and before harvesting. In addition, macro- and microelement contents were determined in the tubers. The results showed that the highest soil microbial biomass contents, dehydrogenase activity, and humus contents were found before potato planting in a conventional farming system. However, from potato planting until the end of the growing season, these soil biological indicators significantly decreased in the soil of conventional farming, but significant increases were recorded in organic and biodynamic treatments. The highest contents of all tested nitrogen forms, phosphorus and potassium, were found in the middle of the potato growing season in a conventional farming system. Before harvesting, significant decreases in all studied agrochemical soil quality indicators were observed in all farming systems. The organic and biodynamic potatoes contained significantly more K, P, and Ca than conventional potatoes. In addition, organic samples had significantly higher contents of Mg, Fe, Mn, Zn, and B in comparison to the biodynamic and conventional ones. The cultivar effect on the content of selected minerals in the samples was also observed. Red Emmalie contained more K, N, and B. Salad Blue had the highest contents of Fe, Mn, and Zn in comparison to other studied cultivars.