Certain plants have specific seasons in their growing cycle that are best for digging and dividing, or transplanting. Peonies are best dug in the fall after it has gotten cold both day and night. Once the foliage has begun to turn burgundy, you know the plants are ready to be disturbed.
Digging established plants can be a real challenge. We find it easiest to use what we refer to as a digging fork. It gets around the roots while loosening it from the soil. Shovels or spades would also work but it is more work getting the roots free of the soil. Ultimately you want a bare root plant.
Once the plant has been extracted from the ground, do your best to knock off all the soil. You can be rough here. We often stand the fork in the ground and pound the base of the roots on the handle. Some roots may break off, that is not a problem. The goal is to have a clear view of the roots so you can see where to pull them apart. You can cut the foliage off any any time.
The soil is mostly off now and you can see the new buds emerging at the crown of the plant. The crown is the term used for the juncture of roots and stem growth. These buds are often referred to as eyes. Peony roots and the crown are tough and woody as opposed to being soft and fleshy.
Now you have your clump of roots. They seem to be all entangled and connected. Think of this as an unraveling challenge. If you wiggle the whole mess you will feel some of the spaces between roots opening up. Keep working those until you can break some free. Breaking the crown is perfectly OK. Be sure each root section has at least 3 eyes. Those eyes will grow into stems next year.
Once you have enough clumps to work with start planting. The roots may be long and unmanageable. Go ahead and cut them back to about 6 inches in length. Dig a hole in a sunny site that has good drainage. No need to add fertilizer now, do that in the spring. Bury the roots with the eyes 2 inches below the soil surface. Lightly mulch the first year if you want and water them in.
If you need to move your peony only temporarily due to construction or refiguring the landscape, you do not need to bareroot the plant if you don’t want to. Instead just dig the whole plant out and heel it in a spot in your vegetable garden. If it cannot be planted immediately in the spring then you will need to either leave it there until the fall or dig it first thing in the spring and put it in a pot. Do not divide it in the spring.