Size-reduction units, size-reduction machines, and methods capable of producing size-reduced products from a variety of solid and semisolid materials. A size-reduction unit includes a circular cutter adapted and arranged to cut a product into strips, a rotating cross-cutter adapted and arranged to receive the strips from the circular cutter, and a stripper plate. The cross-cutter has knives with cutting edges that are adapted and arranged to cut the strips into a size-reduced product, and the stripper plate defines a shear edge in proximity to the cutting edge of each knife of the cross-cutter as its cutting edge encounter the shear edge during rotation of the cross-cutter. The cross-cutter has a helical fluted shape comprising flutes between adjacent pairs of the knives.