A wet process for cleaning biomass is disclosed, comprising: introducing biomass feedstock to a vibrating separator, to generate an overflow stream and an underflow stream, wherein the overflow stream comprises biomass and large grit, and wherein the underflow stream comprises fines and small grit; introducing the overflow stream to a kinetic separator, to generate an intermediate biomass stream and a large-grit stream; introducing the underflow stream and elutriation water to a hydroclone separator, to generate a wet biomass-fines stream and a small-grit stream; separating water contained in the wet biomass-fines stream and recycling it as elutriation water, to generate a biomass fines stream; and combining the biomass fines stream with the intermediate biomass stream, thereby generating clean biomass. An alternative embodiment for a dry process to clean biomass is also disclosed. The clean biomass may be used in a wide variety of biorefining processes.