Soft-stemmed perennials like peonies can be propagated by cuttings---provided that you cut far enough down the stem. Peony stems start in "eyes" that emerge from rhizomes just under the surface of the soil. Cuttings of the rhizome and growing from seed are the reliable ways to propagate these perennials. Rhizome cuttings, unlike seed-grown plants, generally bloom within a season or two of planting and always produce a plant identical to its parent. Make cuttings in the fall for spring blooms.
Make a bushel basket or two of amended soil to fill planting holes; combine garden soil and peat moss, compost or manure in equal measure. Add a handful of bone meal, superphosphate or some other low-nitrogen fertilizer in each bushel of filler. Dig a hole about two feet deep and one foot square for each "division" or new plant---try to estimate the number you will have. You can always fill unused holes with soil. Give each plant about three feet of space on each side.
Choose a day when the soil is moist, not dry, to start; if peony roots dry out, the plant will be set back and may not bloom next season. Dig peonies in the fall after clearing away summer mulch and cutting back dying foliage. Dig deeply underneath the roots with a spade or garden fork all the way around in order to lift the entire root ball. Once the ball is lifted, knock as much dirt off as possible using a hand cultivator or trowel. Work on one plant at a time if digging more than one peony.
Gently clean the remaining dirt away from the rhizome---the fleshy root---and roots. Find the little eyes on the top half of the rhizomes. Be careful to avoid breaking any buds. These are the stem bases for new peony growth and, once broken, will not re-grow.
Cut each rhizome into several pieces with a sharp knife. Each piece must have three to five eyes and a set of roots. Dust each section of the rhizome with an anti-fungal powder, available at most garden centers. If the peony that you are dividing is very old or very large, keep the roots moist with a spray bottle as you cut the rhizome.
Discard any sections with discolorations or rot and trim older or broken roots on divisions. Remove mushy roots---they may have "root rot" or nematodes. Suspend the rhizome over the hole and spread roots while filling the holes with amended soil. Set the rhizome so that the eyes sit no deeper than an inch or so beneath the surface when the hole is filled. Eyes buried deeper than two inches probably will not bloom. Plants should be set no deeper than an inch and a half in southern growing zones. When the hole is filled, water the new plant well.