Cytoplasmic dynein-1 is a minus-end-directed motor protein that transports cargo over long distances and organizes the intracellular microtubule (MT) network. How dynein motor activity is harnessed for these diverse functions remains unknown. Here, we have uncovered a mechanism for how processive dynein-dynactin complexes drive MT-MT sliding, reorganization, and focusing, activities required for mitotic spindle assembly. We find that motors cooperatively accumulate, in limited numbers, at MT minus-ends. Minus-end accumulations drive MT-MT sliding, independent of MT orientation, resulting in the clustering of MT minus-ends. At a mesoscale level, activated dynein-dynactin drives the formation and coalescence of MT asters. Macroscopically, dynein-dynactin activity leads to bulk contraction of millimeter-scale MT networks, suggesting that minus-end accumulations of motors produce network-scale contractile stresses. Our data provide a model for how localized dynein activity is harnessed by cells to produce contractile stresses within the cytoskeleton, for example, during mitotic spindle assembly.