I'd assume that the 4-5" branches remaining are the dead stalks from last season, which could've been cut way back last fall anyway. There 'should' be no problem with it returning. If you look closely at the base, or carefully scoop away any mulch, you should see some dark pink finger tip like growth.

Scoot the mulch back after checking it out.

Sue

I live in the woods with lots of deer and have never had them even sample my peonies. Are they eating your other plants? Al

They are eating ALL of my plants. It was a bad year for my hostas, my smaller younger trees and even some of my barberry. Deer resistant plants are not so in my yard. Thanks for the help!

Are your plants tree peonies or herbaceous peonies? When you said branches in the original post, it made me think of tree peonies. I have heard of them eating tree peonies before, but they usually don't bother the herbaceous ones.

It seems obvious that deer hungry enough will eat anything not poisonous. In my opinion you will have to fence them out if you are to garden where you are. A large dog left out at night is effective but usually also requires a fence. Al