Embodiments provide a cutting system for the stump grinder including a cutting assembly configured to be coupled to a wheel on the stump grinder. The cutting assembly may include a mounting block and a cutting block. The mounting block may be disposed in a pocket of the wheel that extends inward from a circumferential outer edge of the wheel. The cutting block may be coupled to the mounting block. The cutting block may have a continuous cutting edge that extends from a first side of the wheel to a second side of the wheel around a circumferential outer edge of the wheel.