More information please (size of tree, how many branches, picture would be good) - you can't 'trim' a Cordyline, unless you're clipping off soft sprouts of growth at the base or up the trunk you don't want, which I suppose might count as trimming, except you're taking the whole growth off.

Trimming generally implies clipping the outer parts of a plant, and you can't clip the leaves on a Cordyline. You can, though, prune by removing whole branches back to the trunk with a saw, at an angle to allow rain to run off.