Devoid of all known canonical actin-binding proteins, the prevalent parasite Giardia lamblia uses an alternative mechanism for cytokinesis. Unique aspects of this mechanism can potentially be leveraged for therapeutic development. Here, live-cell imaging methods were developed for Giardia to establish division kinetics and the core division machinery. Surprisingly, Giardia cytokinesis occurred with a median time that is ∼60 times faster than mammalian cells. In contrast to cells that use a contractile ring, actin was not concentrated in the furrow and was not directly required for furrow progression. Live-cell imaging and morpholino depletion of axonemal Paralyzed Flagella 16 indicated that flagella-based forces initiated daughter cell separation and provided a source for membrane tension. Inhibition of membrane partitioning blocked furrow progression, indicating a requirement for membrane trafficking to support furrow advancement. Rab11 was found to load onto the intracytoplasmic axonemes late in mitosis and to accumulate near the ends of nascent axonemes. These developing axonemes were positioned to coordinate trafficking into the furrow and mark the center of the cell in lieu of a midbody/phragmoplast. We show that flagella motility, Rab11, and actin coordination are necessary for proper abscission. Organisms representing three of the five eukaryotic supergroups lack myosin II of the actomyosin contractile ring. These results support an emerging view that flagella play a central role in cell division among protists that lack myosin II and additionally implicate the broad use of membrane tension as a mechanism to drive abscission.