Six morpholine-(iso)thiosemicarbazone hybrids HL¹–HL⁶ and their Cu(II) complexes with good-to-moderate solubility and stability in water were synthesized and characterized. Cu(II) complexes [Cu(L^1–6)Cl] (1–6) formed weak dimeric associates in the solid state, which did not remain intact in solution as evidenced by ESI-MS. The lead proligands and Cu(II) complexes displayed higher antiproliferative activity in cancer cells than triapine. In addition, complexes 2–5 were found to specifically inhibit the growth of Gram-positive bacteria Staphylococcus aureus with MIC₅₀ values at 2–5 μg/mL. Insights into the processes controlling intracellular accumulation and mechanism of action were investigated for 2 and 5, including the role of ribonucleotide reductase (RNR) inhibition, endoplasmic reticulum stress induction, and regulation of other cancer signaling pathways. Their ability to moderately inhibit R2 RNR protein in the presence of dithiothreitol is likely related to Fe chelating properties of the proligands liberated upon reduction.