Stomatocytes are polymersomes with an infolded bowl-shaped architecture. This internal cavity is connected to the outside environment via a small 'mouth' region. Stomatocytes are assembled from diamagnetic amphiphilic block-copolymers with a highly anisotropic magnetic susceptibility, which permits to magnetically align and deform the polymeric self-assemblies. Here we show the reversible opening and closing of the mouth region of stomatocytes in homogeneous magnetic fields. The control over the size of the opening yields magneto-responsive supramolecular valves that are able to reversibly capture and release cargo. Furthermore, the increase in the size of the opening is gradual and starts at fields below 10 T, which opens the possibility of using these structures for delivery and nanoreactor applications.