This is common question. Your cordyline will end up as a tree so as it forms a trunk the lower leaves will yellow and die. As they turn brown, pull them off in a downward motion to reveal a bare stem. Some of the garden centres cut the leaves off but to pull them makes a better job in my opinion.

I agree. I had mine for years. It got to over 6 feet and then seemed to die..... I didn't throw it. Left it in the pot at the back of the garden. Hey presto... The next year it sprouted shoots at the base. I pulled out the old trunk. Now I have a lovely new plant to grow on again.
One bit of advice. Remember to tie up the leaves if snow is forecast. As the weight of it can snap them.