Precision placement and transport of biomolecules are critical to many single-molecule manipulation and detection methods. One such method is nanopore sequencing, in which the delivery of biomolecules towards a nanopore controls the method's throughput. Using all-atom molecular dynamics, here we show that the precision transport of biomolecules can be realized by utilizing ubiquitous features of graphene surface-step defects that separate multilayer domains. Subject to an external force, we found that adsorbed DNA moved much faster down a step defect than up, and even faster along the defect edge, regardless of whether the motion was produced by a mechanical force or a solvent flow. We utilized this direction dependency to demonstrate a mechanical analogue of an electric diode and a system for delivering DNA molecules to a nanopore. The defect-guided delivery principle can be used for the separation, concentration and storage of scarce biomolecular species, on-demand chemical reactions and nanopore sensing.