Despite curcumin (CUR) inhibiting cell proliferation in vitro by activating apoptotic cell death, its use in pharmacological therapy is hampered by poor solubility, low stability in biological fluids, and rapid removal from the body. Therefore, CUR-derivatives with better biological and chemical–physical characteristics are needed. The bis-ketone moiety of CUR strongly influences its stability in slightly alkaline solutions such as plasma. Here, we considered its replacement with isoxazole, beta-enamine, or oxime groups to obtain more stable derivatives. The evaluation of the chemical–physical characteristics showed that only of the isoxazole derivatives 2 and 22 had better potential than CUR in terms of bioavailability. The UV–visible spectrum analysis showed that derivatives 2 and 22 had better stability than CUR in solutions mimicking the biological fluids. When tested on a panel of cell lines, derivatives 2 and 22 had marked cytotoxicity (IC50 = 0.5 µM) compared with CUR only (IC50 = 17 µM) in the chronic myeloid leukemia (CML)-derived K562 cell line. The derivative 22 was the more selective for CML cells. When administered at the average concentration found for CUR in the blood of patients, derivatives 2 and 22 had potent effects on cell cycle progression and apoptosis initiation, while CUR was ineffective. The apoptotic effect of derivatives 2 and 22 was associated with low necrosis. In addition, derivative 22 was able to reverse drug resistance in K562 cells resistant to imatinib (IM), the reference drug used in CML therapy. The cytotoxicity of derivative 22 on IM-sensitive and resistant cells was associated with upregulation of FOXN3 and CDKN1A expression, G2/M arrest, and triggering of apoptosis. In conclusion, derivative 22 has chemical–physical characteristics and biological effects superior to CUR, which allow us to hypothesize its future use in the therapy of CML and CML forms resistant to IM, either alone or in combination with this drug.