An improved cutting head for a food product on a slicing machine including upper and lower mounting rings, a plurality of cutter support segments connected to the mounting rings, a cutting blade attached to a front edge portion of each cutter support segment, and opposed first and second pivot pins extending from upper and lower portions of the cutter support segment and through the upper and lower mounting rings. Each of the pivot pins are positioned at a location closely adjacent to a forward edge of the cutter support segment and substantially near a cutting edge of the cutting blade.