The coexistence of leishmaniasis, Chagas disease, and neoplasia in endemic areas has been extensively documented. The use of common drugs in the treatment of these pathologies invites us to search for new molecules with these characteristics. In this research, we report 16 synthetic chalcone derivatives that were investigated for leishmanicidal and trypanocidal activities as well as for antiproliferative potential on eight human cancers and two nontumor cell lines. The final compounds 8–23 were obtained using the classical base-catalyzed Claisen–Schmidt condensation. The most potent compounds as parasiticidal were found to be 22 and 23, while compounds 18 and 22 showed the best antiproliferative activity and therapeutic index against CCRF-CEM, K562, A549, and U2OS cancer cell lines and non-toxic VERO, BMDM, MRC-5, and BJ cells. In the case of K562 and the corresponding drug-resistant K562-TAX cell lines, the antiproliferative activity has shown a more significant difference for compound 19 having 10.3 times higher activity against the K562-TAX than K562 cell line. Flow cytometry analysis using K562 and A549 cell lines cultured with compounds 18 and 22 confirmed the induction of apoptosis in treated cells after 24 h. Based on the structural analysis, these chalcones represent new compounds potentially useful for Leishmania, Trypanosoma cruzi, and some cancer treatments.