Mitochondrial fission is controlled by dynamin proteins, the dysregulation of which is correlated with diverse diseases. Fission dynamins are GTP hydrolysis-driven mechanoenzymes that self-oligomerize into helical structures that constrict membrane to achieve fission, but details are not well understood. However, dynamins can also remodel membranes by inducing negative Gaussian curvature, the type of curvature required for completion of fission. Here, we examine how these drastically different mechanisms synergistically exert their influences on a membrane, via a mechanical model calibrated with small-angle X-ray scattering structural data. We find that free dynamin can trigger a “snap-through instability” that enforces a shape transition from an oligomer-confined cylindrical membrane to a drastically narrower catenoid-shaped neck within the spontaneous hemi-fission regime, in a manner that depends critically on the length of the confined tube. These results indicate how the combination of dynamin assembly, and paradoxically disassembly, can lead to diverse pathways to scission.TeaserDynamin mechano-constriction by assembly and curvature-driven instability by free monomers synergistically drive mitochondrial fission.