That's the normal appearance of Dracaena marginata after a few years of growth:
Dragon Tree (Dracaena reflexa var. angustifolia)
Dragon Tree (Dracaena reflexa var. angustifolia 'Tricolor')
If all of the stems are coming from one trunk at the base, I would trim them one at a time, so the recovery does not require the plant to do it without any foliage. If each stem is separate as it emerges from the soil, trimming all at the same time would be fine since they are separate individuals.
Either way, one or more new stems will grow near the point where each stem is cut. The removed pieces can be stuck back in the pot, all the way to the bottom if they are long enough, to make the pot more full, or in separate pots to start new pots if desired.