In 2020, breast cancer became the most frequently diagnosed type of cancer, with nearly 2.3 million new cases diagnosed. However, with early diagnosis and proper treatment, breast cancer has a good prognosis. Here, we investigated the effect of thiosemicarbazide derivatives, previously identified as dual inhibitors targeting topoisomerase IIα and indoleamine-2,3-dioxygenase 1 (IDO 1), on two distinct types of breast cancer cells (MCF-7 and MDA-MB-231). The investigated compounds (1–3) selectively suppressed the growth of breast cancer cells and promoted apoptosis via caspase-8- and caspase-9-related pathways. Moreover, these compounds caused S-phase cell cycle arrest and dose-dependently inhibited the activity of ATP-binding cassette transporters (MDR1, MRP1/2 and BCRP) in MCF-7 and MDA-MB-231 cells. Additionally, following incubation with compound 1, an increased number of autophagic cells within both types of the investigated breast cancer cells was observed. During preliminary testing of ADME-Tox properties, the possible hemolytic activities of compounds 1–3 and their effects on specific cytochrome P450 enzymes were evaluated.