Triple negative breast cancer (TNBC) is characterized by clinical aggressiveness, lack of recognized target therapy, and a dismal patient prognosis. Several studies addressed genomic changes occurring during neoadjuvant chemotherapy (NAC) focusing on somatic variants, but without including copy number alterations (CNAs). We analyzed CNA profiles of 31 TNBC primary tumor samples before and after NAC and of 35 single circulating tumor cells (CTCs) collected prior, during and after treatment by using next-generation sequencing targeted profile and low-pass whole genome sequencing, respectively. In pre-treatment tissue samples, the most common gains occurred on chromosomes 1, 2 and 8, and SOX11 and MYC resulted the most altered genes. Notably, amplification of MSH2 (4/4 versus 0/12, p < 0.01) and PRDM1 and deletion of PAX3 (4/4 versus 1/12, p < 0.01) significantly characterized primary tumors of patients with pathological complete response. All patients with paired pre- and post-NAC samples reported a change in post-treatment CNAs compared to baseline, despite they showed at least one common alteration. CNAs detected after treatment involved genes within druggable pathways such as EGFR, cell cycle process and Ras signaling. In two patients, CTCs shared more alterations with residual rather than primary tumor involving genes such as MYC, BCL6, SOX2, FGFR4. The phylogenetic analysis of CTCs within a single patient revealed NAC impact on tumor evolution, suggesting a selection of driver events under treatment pressure. In conclusion, our data showed how chemoresistance might arise early from treatment-induced selection of clones already present in the primary tumor, and that the characterization of CNAs on single CTCs informs on cancer evolution and potential druggable targets.