Multi-layer sheets of graphene-based material having a plurality of pores extending therethrough are described herein. Methods for making the sheets include exposing a graphene-based material comprising multilayer graphene having from 5 to 20 layers of graphene to a particle beam having an ion energy of at least about 1500 eV to create damage tracks in the graphene sheets. The damage tracks in the graphene sheets are then exposed to a chemical etchant, such as an oxidant to define pores through the stacked graphene sheets. Production of the damage tracks and etching of the damage tracks can take place while the graphene is disposed on a substrate.