Machines and methods suitable for performing cutting operations on a product to yield a reduced-size product, for example, slicing and strip-cutting elongate food products. Such a method includes introducing a product into an impeller, rotating the impeller to form at least a first longitudinal cut through the product with a slicing knife and produce therefrom a sliced product, and producing strip-cut products from the sliced product by forming at least a second longitudinal cut that is substantially perpendicular to the first longitudinal cut made with the slicing knife.