Tree Peonies can be split by digging up the entire plant, rinsing off the roots and dividing it using a sharp knife or pruners, being sure to leave adequate roots on each of the divisions. Cut the canopy back to lession the transplant shock. Dig the hole and generously amend the backfill material with organic matter and water well at transplant time and monitor for water needs during the the weeks following the transplanting.
Sincerely, Richard