If you have a silver birch tree stump in your yard and you want to make sure the root system does not allow the stump to start growing again, you need to kill the root system. The easiest way to do this is to rot the stump. The stump will then rot the root system of the tree. With the roots dead, the tree will no longer attempt to grow.
Cut the birch tree stump as close to the ground as you can with a chainsaw.
Drill as many holes as you can into the top of the trunk with a hand drill equipped with the largest drill bit you have.
Fill the holes in the trunk with water and then fill the holes with a nitrogen-rich fertiliser.
Water the trunk and the ground surrounding the trunk and then place a plastic tarp over the area.
Cover the tarp with mulch and then wet the mulch. The mulch will help to keep the tarp on and hold moisture against the trunk.
Remove the fertilisers and tarp from the stump weekly. Replace the fertiliser with fresh fertiliser and wet the area again with the hose. Restore the tarp and mulch. Do this weekly until you can break the trunk apart with your hands. This will ensure the trunk rotted down to the root system.