Although genomic sequencing has provided a better understating of the genetic landmarks in triple-negative breast cancer (TNBC), functional validation of candidate cancer genes (CCG) remains unsolved. In this study, we used a transposon mutagenesis strategy based on a two-step sleeping beauty (SB) forward genetic screen to identify and validate new tumor suppressors (TS) in this disease. We generated 120 siRNAs targeting 40 SB-identified candidate breast cancer TS genes and used them to downregulate expression of these genes in four human TNBC cell lines. Among CCG, whose SB-mediated genetic mutation resulted in increased cellular proliferation in all cell lines tested, the genes ADNP, AP2B1, TOMM70A, and ZNF326 showed TS activity in tumor xenograft studies. Subsequent studies showed that ZNF326 regulated expression of multiple epithelial-mesenchymal transition and cancer stem cell (CSC) pathway genes. It also modulated expression of TS genes involved in the regulation of migration and cellular invasion and was a direct transcriptional activator of genes that regulate CSC self-renewal. ZNF326 expression associated with TNBC patient survival, with ZNF326 protein levels showing a marked reduction in TNBC. Our validation of several new TS genes in TNBC demonstrate the utility of two-step forward genetic screens in mice and offer an invaluable tool to identify novel candidate therapeutic pathways and targets.