You can kill almost anything by putting a sheet of heavy black plastic over it for a while. This deprives it of light and water, and the heat cooks it. The downside is you will end up with a completely dead area.
Since this does not disrupt the ground cover you could allow the area to recover naturally but I would suggest using good judgement over how large an area you do this to. I have only done this on flat areas.
I found this out by accident one year when I laid out sections of roofing paper for a shed I was building. This technique saved me from renting heavy equipment to pull some hedges when my grandfather decided to switch to a fence. I trimmed the hedge to the ground level and laid the cover about a foot to either side of the stumps. That cover, I left down for a couple months to be certain. There was over 200 feet of hedge and none of it grew back.
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