Cut the side branches of the holly bush with a chain saw to access the main trunk without getting poked by the sharp leaves. Make a horizontal cut through the trunk 3 inches from the ground with the chain saw.
Remove rocks and debris from around the holly bush to protect the stump grinder's wheel.
Drive a stump grinder to the edge of the holly stump. Lift the wheel up 3 inches above the stump using the hydraulic lever. When operating a stump grinder, remain on the side of the machine whenever the wheel is in use.
Lower the stump grinder's wheel so that it grinds through the stump from side to side to a depth of 4 inches. Lift up the wheel 3 inches from the stump and advance the stump grinder forward. Grind up the rest of the stump.
Fill the hole with soil. Pick up all pieces of the holly bush from the lawn to compost or throw away.