A demolition/scrap processing shears assembly includes pivotally connected jaws. The first jaw has first and second laterally-spaced shearing edges. The second jaw has third and fourth laterally-spaced shearing edges. The first and second shearing edges have a plurality of staggered shearing apexes that sequentially shearingly mate with the third and fourth shearing edges, respectively, as the shear assembly closes. As viewed from the side, the third and fourth shearing edges are offset from each other such that the first and third shearing edges shearingly mate with each other asynchronously relative to the second and fourth shearing edges as the jaws close. Staggering the shearing apexes and offsetting the shearing action of the left and right side of the shear assembly reduces the power that an actuator must generate to shear processed material.