use a sharp knife... to cut a small firm section of the oldplant & some of the living roots OR cut new growth from old stem. let it air dry then apply 0.1% IBA (rooting hormone. stick in damp well drained soil. will root in 2-6 weeks.

Personally if the new shoots are not too far above ground level, I'd just cut off the old stem an inch or so above the top one and leave them on the old stem base. Dracenas are quite attractive as multicaned plants.

George

Geoforce is correct. Just lop of the dead area and let the new shoot grow, it's a good way to maintain height and make them more bushy. It may take awhile, but new shoots will grow even if you tip off a healty branch. Just keep it indoors or protected from cold harsh elements.