In one aspect, a cutter system for a waste disposal may generally include a cutter ring having an upper surface and a lower surface. In addition, the cutter ring may define a plurality of cutter slots. Each cutter slot may extend between a top end and a bottom end and may be defined by a first curved sidewall and a second curved sidewall. The first and second curved sidewalls may extend between the top and bottom ends such that each cutter slot defines a curved profile extending axially and circumferentially between the upper and lower surfaces of the cutter ring.