A waste separator apparatus is provided. The apparatus includes a first screen assembly for screening fluids from a waste stream where the first screen assembly defining an enclosure. A second screen assembly is provided for screening fluids from the waste stream and is disposed closely spaced-apart within the enclosure of the first screen assembly. A waste stream pathway is defined between the first screen assembly and the second screen assembly. A first separated fluids stream pathway is defined outwardly of the first screen assembly. A second separated fluids stream pathway is defined inwardly of the second screen assembly. One or more blades extends inwardly from the first screen assembly or outwardly from the second screen assembly for advancing the waste stream through the waste stream pathway. A related system is also provided.