Blackberry bushes are tough garden invaders to get rid of, as burning or mowing the plant just encourages it to grow more! It is a prickly, brambly plant that grows rapidly. One of the best and least expensive ways to remove a blackberry bush is to completely remove the plant, fragments and roots by hand, and dissolve the stump with boiling water.
Put on the gardening gloves to protect your hands from the sharp brambles. Use pruning shears to cleanly cut the stump off near the ground. Remove them as quickly as possible so the roots don't start to spread.
Take a shovel and dig deep down the side of the stump to pull it out. You want to completely remove the stump. This will probably rip up the roots, so you'll need to hand-pick the root fragments out where ever you can find them. Discard everything that is dug up.
Boil two gallons of water and pour it over the area that you removed the blackberry bush from. Do this over the course of the day, about three to five times. Doing this helps waterlog the root system and any parts left, which will make it start to rot.
Use a till on the area over and over to get rid of any root pieces, rhizomes and fragments from the bush. Do this multiple times over the course of a couple days, and discard whatever is dug up.