A screw-type centrifugal pump with scissoring back cutters and having a housing with an intake opening and an outlet opening, both in fluid communication with an internal chamber, and an impeller assembly positioned within the chamber, is disclosed. Generally speaking, the impeller assembly has a hub having a back shroud and being attached to a rotatable pump shaft, with an impeller attached to the hub. An insert cutter positioned on a surface of the hub shroud opposite the impeller includes a cutting edge configured for shearing operation, while a stationary back plate having a surface adjacent to and facing the hub shroud includes a cutting rib having a cutting edge configured for shearing operation. The insert cutter and cutting rib work jointly to create a cutting action as the hub rotates in the chamber.