Had a similar problem with the previous workshops. The problem was that the main stem was between the shop and the fence, so VERY difficult to cut off near the ground.
A saw blade fixed to a long pole did the trick, eventually.
Now the problem is one of SWMBOs plants that can cause heave depending on the weather, making the door stick sometimes. What started as a tiny stem is now nearly 100 mm diameter, but cannot be pruned other than gently.
Ivy seems to share some of the genes of Mile a Minute Russian Vine., and is very difficult to keep in check
SWMBO put some weedkiller on the grass,(Supposed to be safe for grass ) Killed the grass as well as the weed, A year on it still has not recovered, despite reseeding. This might be the stuff to put on the root, if you can dribble some down a tube into the area. "Weedol" perhaps?
Squirt from a water pistol may get the killer where it is needed.
Howard