Centrosome amplification (CA) is a hallmark of cancer that is strongly associated with highly aggressive disease and worse clinical outcome. However, there are no effective strategies targeting cancer cells with CA while sparing normal cells. Here, we identified Transforming Acidic Coiled-Coil Containing Protein 3 (TACC3) to be overexpressed in tumors with CA, and its high expression is associated with dramatically worse clinical outcome. We demonstrated that TACC3 forms distinct functional interactions in mitotic and non-mitotic cancer cells with CA to facilitate centrosome clustering (CC) and transcriptional repression of tumor suppressors, respectively. We showed, for the first time, that TACC3 interacts with the Kinesin Family Member C1 (KIFC1) via its TACC domain in mitotic cells with CA and inhibition of TACC3 blocks this interaction, leading to apoptosis via multipolar spindle formation and activation of spindle assembly checkpoint (SAC)/CDK1/p-Bcl2 axis. In interphase, TACC3 interacts with the members of the nucleosome remodeling and deacetylase (NuRD) complex (HDAC2 and MBD2) in nucleus, and its inhibition causes p53-independent G1 arrest and apoptosis by blocking these interactions and activating the transcription of key tumor suppressors (e.g., p21, p16 and APAF1). Notably, inducing CA by chemical (cytochalasin D) or genomic (PLK4 overexpression or p53 loss) modulations renders cancer cells highly sensitive to TACC3 inhibition. Targeting TACC3 by small molecule inhibitors or guide RNAs strongly inhibits growth of organoids and breast cancer cell line- and patient-derived xenografts with CA. Altogether our results pave the way towards therapeutic targeting of TACC3 in highly aggressive cancers.