During cell division, the microtubule nucleating and organizing organelle, known as the centrosome, is a critical component of the mitotic spindle. In cells with two centrosomes, each centrosome functions as an anchor point for microtubules, leading to the formation of a bipolar spindle and progression through a bipolar cell division. When extra centrosomes are present, multipolar spindles form and the parent cell may divide into more than two daughter cells. Cells that are born from multipolar divisions are not viable, and hence clustering of extra centrosomes and progression to a bipolar division are critical determinants of viability in cells with extra centrosomes. We combine experimental approaches with computational modeling to define a role for cortical dynein in centrosome clustering. We show that centrosome clustering fails and multipolar spindles dominate when cortical dynein distribution or activity is experimentally perturbed. Our simulations further reveal that centrosome clustering is sensitive to the distribution of dynein on the cortex. Together, these results indicate that dynein's cortical localization alone is insufficient for effective centrosome clustering and, instead, dynamic relocalization of dynein from one side of the cell to the other throughout mitosis promotes timely clustering and bipolar cell division in cells with extra centrosomes.