Examine the location of the tree. Hire a professional tree removal service if the eucalyptus grows near a building or is over 6 feet tall. Choose to cut the tree down on a sunny day when the ground is wet. Avoid using electric cutting equipment when the ground is wet from rainfall.
Measure the largest part of the tree trunk. Trunks that measure 6 inches or less in diameter can be directed easily. Trees with trunks wider than 6 inches should be felled by professional companies.
Wear safety goggles and gloves before starting your tree removal. Wear a breathing mask if you have allergies to eucalyptus. Make a cut at the base of the tree one-third of the way into the trunk. Cut back and forth with a handsaw or use a chainsaw to make the slice. This is called a back slice.
Move to the other side of the tree. Using your saw, make a cut into the tree at a 45-degree angle. Make a second cut, horizontally under the angled cut. This will result in a triangular cutout shape. This is called an undercut.
Alternate cuts from the back cut to the undercut until the tree begins to lean. Allow the tree to fall, and cut the tree into firewood or load it up as rubbish.