Only if you can get a good piece of root with the new shoots - otherwise, leave them alone and let them grow on into a new cordyline.

Ok thanks for that now on same plant i am going to do as you sugessted and let the shoots grow but i have 3foot 6 inches of dead trunk and i realy wish to transfer the whole plant to other side of garden where it will get more sunlight,so am dubious as what to cut of on the trunk with out causing damage

Cut the trunk right down to wherever the new growth has appeared (I'm assuming its coming out the bottom of the trunk). If you make it an angled cut to allow rain to run off, so much the better. As for moving it, if its been in longer than 3 years, a very risky business, you may lose it, but if you want to try, you need to keep a good rootball and extract carefully all the longer roots when digging it out, without breaking any, and make sure the new hole is the right shape and depth to accommodate the roots without cramping them up. And water thoroughly afterwards, best done in late September.