You can also just yank out the herbacious stock when it comes up. It can weaken a tree peony plant by giving energy to the herbacious stock, rather than just giving energy to the tree peony.
They say that on an older enough tree peony, it has grown enough of its own roots to actually cut the herbacious root stock off of it by digging the whole plant up. The roots are much different and are very easy to discern. That said, I haven't done it myself. I've just listened to wise growers tell me how to do it.
I find yanking the herbaceous growth out as it comes out to work just fine. The tree peony I speak of is planted plenty deep, I have just been told that the root stock is adventitious and doesn't even need eyes to grow! Most US growers don't use this type of root stock.
