What you are seeing is a so called "compound disease", meaning there's more than one disease at work.
In peonies that condition is usually due to one virus infection (usually a Tobravirus, as they are the ones most likely to infect peonies) and one or two fungal diseases: that's what makes identifying the exact nature of these issues so difficult using commonly available literature.
Without costly genetic tests there's no way to know exactly what you are dealing with, but the cure is always the same: dig up and destroy that plant. Do not compost it.
For more bad news, if all your other plants are healthy you were most likely sold infected stock. It can happen and more often than not the nursery carries no blame, as they usually just sell plants they bought in bulk from a commercial grower. However it's good practice to let the nursery owners know, especially if you still have the ID of the plant you were sold.
Most diseases affecting peonies are transmitted by nematodes but simply digging up the soil and looking for them won't get you nowhere as most of them are invisible to the naked eye. And besides that, while several are truly nasty little chaps, most nematodes found in the ground are harmless.
Nematocides are available but they aren't exactly eco-friendly stuff and require both dedicated equipment and expertise to be applied.
The best ecofriendly solution is to plant French marigolds (Tagetes patula) for two years where the peony was. Marigolds won't do miracles but are well known to dramatically reduce the density of the most harnful nematodes in the ground. Be warned that African marigolds (T. erecta), albeit showier, are nowhere as good as nematocides.
