The shape of biological matter is central to cell function at different length scales and determines how cellular components recognize, interact and respond to one another. However, their shapes are often transient and hard to reprogramme. Here we construct a synthetic cell model composed of signal-responsive DNA nanorafts, biogenic pores and giant unilamellar vesicles (GUVs). We demonstrate that reshaping of DNA rafts at the nanoscale can be coupled to reshaping of GUVs at the microscale. The nanorafts collectively undergo reversible transitions between isotropic and short-range local order on the lipid membrane, programmably remodelling the GUV shape. Assisted by the biogenic pores, during GUV shape recovery the locally ordered DNA rafts perforate the membrane, forming sealable synthetic channels for large cargo transport. Our work outlines a versatile platform for interfacing reconfigurable DNA nanostructures with synthetic cells, expanding the potential of DNA nanotechnology in synthetic biology.