Dig around the drip line -- where the stems end -- of a mature myrtle spurge in early spring, just as new growth is beginning on the evergreen plant. Dig 8 to 10 inches deep, about the depth of the head of a standard garden spade, to ensure you don't injure the taproots.
Lift the plant from the soil with the shovel and lay it on its side, exposing the roots, without crushing the top growth.
Knock the soil off the root ball of the plant to expose the crown of the plant and the roots.
Examine the root ball for natural places to separate the plant. Stems lead into a narrow neck with a taproot and small side roots. You will see a clump of branching taproots in a large plant.
Cut the plant into sections, each with a taproot, or part of a taproot, a stem and some side roots. Cut through the sides of the taproots where they branch. Work carefully to avoid damaging the top growth or the roots -- both tend to snap easily.
Dig new holes 6 to 18 inches apart that are just as deep as the new roots and twice as wide in soil that drains well and is in full sun. Spacing depends on how much ground you want to cover and how soon you want to divide the plants again.
Water your new plants well, soaking the soil at the first watering, and providing at least an inch of water each week until new growth begins. Myrtle spurge is drought tolerant once established.