Cordyline species are tropical plants you find outdoors in Hawaii, Australia, New Guinea and other warm regions. The New Zealand native "Cordyline australis" is cold hardy in comparison to others in the same plant group, but it needs protection from frost. In the United States, Cordyline australis is known as cabbage tree and hardy in U.S. Department of Agriculture Zones 10 and 11 only. Elsewhere in the country, the tree grows as a houseplant. Cordyline roots sometimes send out lateral shoots called suckers. Use them to propagate the tree.
Move the soil from around the side shoot carefully in spring to expose the root system in that area. Keep loosening the soil to lift the sucker out of the hole and lower it on the surface. (See References 4)
Cut into the root crown with a sharp knife to separate the lateral shoot from the mother plant.
Backfill the hole next to the main Cordyline with the topsoil you dug. Irrigate the area to the depth of the roots to help them recover from the cutting.
Prune the rhizome, if there is one, attached to the Cordyline shoot. The rhizome is the enlarged horizontal underground stem that links sucker to main plant. It looks tuberous, not fibrous like the roots.
Plant the Cordyline shoot in full sun or partial shade. Place it in the hole at the same depth as it grew as part of the main plant. Refill the hole and firm the surface around the base of the stem. Irrigate the plant to the root zone.