Previous research has indicated the highly expressed lysine‐specific histone demethylase 1A (KDM1A) in several human malignancies, including triple‐negative breast cancer (TNBC). However, its detailed mechanisms in TNBC development remain poorly understood. The mRNA levels of KDM1A and Yin Yang 1 (YY1) were determined by RT‐qPCR analysis. Western blot was performed to measure KDM1A and ubiquitin‐specific protease 1 (USP1) protein expression. Cell proliferation, apoptosis, invasion, migration and stemness were evaluated by MTT assay, EdU assay, flow cytometry, transwell invasion assay, wound‐healing assay and sphere‐formation assay, respectively. ChIP and dual‐luciferase reporter assays were conducted to determine the relationship between YY1 and KDM1A. Xenograft tumor experiment and IHC were carried out to investigate the roles of USP1 and KDM1A in TNBC development in vivo. The highly expressed KDM1A was demonstrated in TNBC tissues and cells, and KDM1A knockdown significantly promoted cell apoptosis, and hampered cell proliferation, invasion, migration, and stemness in TNBC cells. USP1 could increase the stability of KDM1A via deubiquitination, and USP1 depletion restrained the progression of TNBC cells through decreasing KDM1A expression. Moreover, YY1 transcriptionally activated KDM1A expression by directly binding to its promoter in TNBC cells. Additionally, USP1 inhibition reduced KDM1A expression to suppress tumor growth in TNBC mice in vivo. In conclusion, YY1 upregulation increased KDM1A expression via transcriptional activation. USP1 stabilized KDM1A through deubiquitination to promote TNBC progression.