Female breast cancer is one of the leading causes of death among patients with cancer and requires a proactive strategy for a cure. Triple-negative breast cancer (TNBC) is the most aggressive cancer with a high risk of developing metastases. The purpose of the present study was to screen the pharmacological activities of three promising ethacrynic acid (EA) derivatives containing a piperazine moiety (P3, P4, and P5). The EA derivatives were tested against MDA-MB-468 cancer cell line as a model for TNBC and MCF7 cancer cell line as a model subtype of luminal breast cancer using the methyl tetrazolium test (MTT). Additionally, the modulation of the glutathione and thioredoxin systems, as well as the antioxidant and cytoprotective potential of each compound, were investigated. Moreover, initial in vitro safety screening was conducted using human blood cells. As a result, EA derivatives showed clear dose-dependent antiproliferative activity with high selectivity to cancer cells by orchestrating oxidative stress. Derivative P3 has the most promising potential for further preclinical investigation, owing to its safety profile and significant cytoprotective and antitumor properties.