Nano-patterned and suspended graphene membranes find applications in electronic devices, filtration and nano-pore DNA sequencing. However, the fabrication of suspended graphene structures with nanoscale features is challenging. We report the direct patterning of suspended membranes consisting of a graphene layer on top of a thin layer of hexagonal boron nitride which acts as a mechanical support, using a highly focused electron beam to fabricate structures with extremely high spatial resolution within the scanning transmission electron microscope. The boron nitride support enables the fabrication of stable graphene geometries by preventing intrinsic strain in graphene membranes from distorting the patterned features. Line cuts with widths below 2 nm are reported. We also demonstrate that the extent of cutting can be monitored in situ utilising electron energy loss spectroscopy.