Cell division is an essential requirement for life. Division requires mechanical forces, often exerted by protein assemblies from the cell interior, that split a single cell into two. Using coarse-grained computer simulations and live cell imaging we define a distinct cell division mechanism—based on the forces generated by the supercoiling of an elastic filament as it disassembles. Our analysis suggests that such a mechanism could explain ESCRT-III–dependent division in Sulfolobus cells, based on the similarity of the dynamics of division obtained in simulations to those observed using live cell imaging. In this way our study furthers our understanding of the physical mechanisms used to reshape cells across evolution and identifies additional design principles for a minimal division machinery.