We really need to know what the plant is to answer correctly, but I'll take a stab in the dark and guess at its being a Cordyline. If it is, and the main trunk is dead, cut that down if you haven't already. The babies growing from the base usually arise off the base of the trunk, and can only be separated and grown on if you can get ones with roots attached. Otherwise, they'll just grow on as they are into new plants to replace the dead part - if you don't want so many, cut some off and bin them, leaving what you do want behind.