Kent,
United Kingdom 
I was searching for answers on Cordylines and found this page. Both my cordylines(bronze) lost their tops during the bad winter. One we dumped the 2nd is now shooting from the base as we cut it down to the bas of the stem. Can the new shoots be taken off and replanted?
9 Jul, 2010
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Only if you can get some root with them. If they've grown on quite a bit, have a dig around at the base and see if there's much root there and whether you think you can get a very sharp knife, place between the stump and the plantlet and slice downwards, taking a good bit of root with it. Pot up and nurture for a while! Otherwise you can just leave them in situ - they'll carry on growing and make an interestingly shaped Cordyline.
9 Jul, 2010