A rivering filtration system for a power saw machine includes a filtration tray having a filtration cavity for collecting operation fluid after the operation fluid is delivered onto the cutting blade, and a fluid collecting tray located underneath the filtration tray, wherein the fluid collecting tray has first and second cavities. The filtration tray provides a first filtration stage for filtrating the visible residual particles out from the operation fluid. The fluid collecting tray provides a second filtration stage that the operation fluid is slowly filled in the first cavity from the filtration cavity to ensure slurry residual particles in the operation fluid being deposited at the first cavity, and a third filtration stage that the operation fluid is slowly filled in the second cavity from the first cavity to ensure the slurry residual particles being filtrated out of the operation fluid.