Put on safety equipment. Make sure you have a properly fitting hat, boots and glasses. Attach your safety harness correctly. Remove the palm branches and top off the tree. Begin to cut the tree down, starting from the top, in two-foot sections.
Remove as much as the stump as possible. The queen palm trunk should be easy to cut through. Use a small ax to work your way down to as much root as possible. Discard to a wood pile or chipper for recycling.
Dig around the root. If the root is still stubborn, you will have to dig down and around the root ball. Start off about a 2 feet away from the base of the tree until you find the end of the roots. You can also sever off the roots with the shovel and work your way down until the stump or base of the tree ends. Pry the root ball up by digging under and pushing up with the shovel.
Pull the root out completely. If the root base is large, you may have to tie a rope around the midsection of the stump and try to pull the root ball out. If roots are stubborn, use trimmers or loppers to cut away at the roots. Pull out the entire tree and as many visible roots as possible. If the root base is too large to pull manually, you may have to rely on a gas-powered tree spade and backhoe for assistance.
Cover the hole with remaining soil. Use the soil you used to dig around the tree. You may have to bring in fill-dirt or topsoil to fill the hole completely. Plant grass seed or plant another tree if desired.