We created two new mutants of fission yeast cofilin to investigate why cytokinesis in many organisms depends on this small actin-binding protein. These mutant cofilins bound actin monomers normally, but bound and severed ADP-actin filaments much slower than wild-type cofilin. Cells depending on mutant cofilins condensed nodes, precursors of the contractile ring, into clumps rather than rings. Starting from clumped nodes, mutant cells slowly assembled rings from diverse intermediate structures including spiral strands containing actin filaments and other contractile ring proteins. This process in mutant cells depended on α-actinin. These slowly assembled contractile rings constricted at a normal rate but with more variability, indicating ring constriction is not very sensitive to defects in severing by cofilin. Computer simulations of the search-capture-pull and release model of contractile ring formation predicted that nodes clump when the release step is slow, so cofilin severing of actin filament connections between nodes likely contributes to the release step.