Abstract: A stump cutting or grinding apparatus and method are disclosed which utilize a pump for attachment to a power takeoff of a tractor, a cutting or grinding device for attachment to a backhoe arm of the tractor, a motor connected to the cutting or grinding device, a plurality of lines for circulating hydraulic fluid between the pump and the motor and a plurality of lines for passing a portion of the hydraulic fluid through the hydraulic system of the tractor. Passing a portion of the circulating hydraulic fluid through a hydraulic system of the tractor enables the tractor to cool and filter the fluid and eliminates the need for a separate tank or reservoir that would otherwise be needed to contain and treat fluid being circulated between the pump and motor. A scoop may be attached to the cutting or grinding device for moving or removing rocks, dirt or debris from around the stump.