I had a similar experience with a tree peony too. After growing it for several years, a herbaceous peony sprouted right next to it and bloomed. Until then, I had no idea they were grafted. I dug under the soil a bit, and removed the growth and buds I found under there, and didn't have any more issues. It sounds like yours has enough root attached to survive, but I agree with others that pruning back would be a good idea. Best of luck.
