Membrane abscission, the final cut of the last connection between emerging daughter cells, is an indispensable event in the last stage of cell division, as well as in other cellular processes such as endocytosis, virus release, or bacterial sporulation. However, its mechanism remains poorly understood, which also impedes its application as a cell-division machinery for synthetic cells. Here, we use fluorescence microscopy and Fluorescence Recovery After Photobleaching (FRAP) to study the in vitro reconstitution of the bacterial protein Dynamin A (DynA) inside liposomes. Upon external reshaping of the liposomes into dumbbells, DynA self-assembles at the membrane neck, resulting in membrane hemi-scission and even full scission. DynA proteins constitute a simple one-component division machinery that is capable of splitting dumbbell-shaped liposomes, marking an important step towards building a synthetic cell.