Although they can be attractive, acacia trees are also very invasive and can overtake your garden if left to grow unchecked. If you're in the middle of an acacia invasion, you should know that cutting them down isn't enough to kill them. The leftover stumps will continue to grow, and you will be left with acacia shrubs. If you want to completely stop an acacia from growing, you have to kill it at the roots. This can be accomplished using different chemicals.
Avoid working on the tree during spring and early summer -- this is when the tree, even as a stump, will be producing sap, which will prevent the herbicide from reaching the roots.
Cut down the tree. If your tree is very large, near a building, or adjacent to power lines, you will need to hire professional help to remove the tree. Depending on the size of the tree, use loppers, a handsaw or a chain saw to cut it down. Cut the stump as close to ground level as you can.
Spray an herbicide containing either glyphosate or triclopyr at 50-percent concentration over the surface of the stump. Alternatively, drill holes into the top of the stump, and pour rock salt or Epsom salt into the holes. Pour either type of salt in a ring around the stump, and water the area until the crystals dissolve.
Pour another layer of rock salt or Epsom salt around the stump, and water it into the ground. Cover the entire stump with fertile topsoil. This will help rot the stump and attract insects that will eat the stump and roots.