The GTPase dynamin is critically involved in membrane fission during endocytosis. How does dynamin use the energy of GTP hydrolysis for membrane remodeling? By monitoring the ionic permeability through lipid nanotubes (NT), we found that dynamin was capable of squeezing NT to extremely small radii, depending on the NT lipid composition. However, long dynamin scaffolds did not produce fission: instead, fission followed GTPase-dependent cycles of assembly and disassembly of short dynamin scaffolds and involved a stochastic process dependent on the curvature stress imposed by dynamin. Fission happened spontaneously upon NT release from the scaffold, without leakage. Our calculations revealed that local narrowing of NT could induce cooperative lipid tilting, leading to self-merger of the inner monolayer of NT (hemifission), consistent with the absence of leakage. We propose that dynamin transmits GTP's energy to periodic assembling of a limited curvature scaffold that brings lipids to an unstable intermediate.