Dracaenas do propagate easily from cuttings. I have done this to the various ones I have approaching 100 times with no defoliation or failure to root, except the one time I stuck one in water instead of soil. It usually takes about 15 seconds to do, snip stem & stick it in a pot.
This is the root system of one cutting after about a year:
I always devote at least 6" at the bottom of the cutting to submerge into the soil. Since the leaves dangle the way they do, I've always cut far enough down so that the leaves are not touching the soil when that much stem is submerged, so cuttings are usually at least a foot long.
Your plant looks healthy & vigorous. Cutting it would not kill it. New growth would come from the stump, near the point where it was cut. Sometimes there is just 1 new stem, sometimes more. There are various pics of cut trunks regrowing new branches here:
Dragon Tree (Dracaena reflexa var. angustifolia 'Tricolor')