Chromosome movements are linked to the active depolymerization of spindle microtubule (MT) ends. Here we identify the kinesin-13 family member, KLP59D, as a novel and uniquely important regulator of spindle MT dynamics and chromosome motility in Drosophila somatic cells. During prometaphase and metaphase, depletion of KLP59D, which targets to centrosomes and outer kinetochores, suppresses the depolymerization of spindle pole-associated MT minus ends, thereby inhibiting poleward tubulin Flux. Subsequently, during anaphase, loss of KLP59D strongly attenuates chromatid-to-pole motion by suppressing the depolymerization of both minus and plus ends of kinetochore-associated MTs. The mechanism of KLP59D's impact on spindle MT plus and minus ends appears to differ. Our data support a model in which KLP59D directly depolymerizes kinetochore-associated plus ends during anaphase, but influences minus ends indirectly by localizing the pole-associated MT depolymerase KLP10A. Finally, electron microscopy indicates that, unlike the other Drosophila kinesin-13s, KLP59D is largely incapable of oligomerizing into MT-associated rings in vitro, suggesting that such structures are not a requisite feature of kinetochore-based MT disassembly and chromosome movements.