Buckthorn is on the Minnesota DNR’s list of restricted noxious weeds. It is an invasive species that was imported from Europe and used for hedges. You may recall a couple of years ago goats were hired to eat the buckthorn growing in Indian Mounds Park.
This year I found some buckthorn in my yard and my neighbors are growing a large buckthorn bush along a fence. The way to get rid of buckthorn is to pull it out and dig out the roots. The plant I found was fairly small and easy to remove. It was hiding near my lilac bushes.
The plant is fairly easy to identify. When in doubt look for thorns at the base of the leaves where they join the stem.
Buckthorn plants that are two inches in diameter or larger are best controlled by cutting the stem at the soil surface and then covering or treating the stump to prevent re-sprouting. Cutting can be effectively done with hand tools (for a few plants), chain saws or brush cutters.
The Minnesota DNR has a lot of information about the plant and how to remove it. You will need a permit to have goats in your St. Paul yard but I suppose that is an option too.