I have said it before, and I'll say it again:
Mint.

Mint.

Mint, mint, MINT!!!
I never realized how invasive it is! Terrible stuff. I yanked out every plant I saw. I dug down deep and took out roots. I rototilled the garden and pulled out every leaf, stem, and root I saw. I repeated that process two weeks later. And
still there was mint.
For three years now, I've done that - yank, dig, till, sift, ... rinse and repeat ...every spring. It's better, but AAUUGH!!!
Mint.
CrazyConure, mint is invincible. I firmly believe it is impossible to kill mint. (I've tried!)
@Beth_B is right, and I'd try napalm,

but it is right next to the house.
If it's getting too much rain, you might want to move it where it will dry a bit. But you can't kill it.
