A pump having a cutting wheel and a pre-cutter (26) for cutting chippings that are contained in the medium pumped by the pump, the pre-cutter being driven by a shaft portion that projects axially from the cutting wheel and having a plurality of wings (28), the pre-cutter being surrounded by a crest of anvil blocks (32) at which the free ends of the wings (28) move past in a little distance when the pre-cutter rotates, wherein the anvil blocks are configured as counter-blades (32) that are held exchangeably at a blade carrier (34) that surrounds the pre-cutter (26) at least on a part of its periphery.