This is a pic of the same plant showing the 3 shoots I have.

Dracaena comes very easily from tip cuttings, and your branch will back-bud, usually in several places at or near the point of truncation after you separate the cutting.

Best way is to cut through the stem about 8" below the growing tip with a sharp bypass pruner or lopper. After the cut is made, use a razor knife with a new blade to trim both cut ends - the one on the cutting and the one on the plant. Loos pieces of ragged tissue is where rot forms, so make sure the wounds are clean. Use a thin coat of waterproof wood glue (or bonsai cut paste if you know someone who practices bonsai) to cover the wound on the parent plant only. Strip the leaves from the cutting so there are only a few leaves left on the tip, and stick the cutting in a fast draining medium you can keep moist but not wet. If the leaves are very large, you might need to cut them in half across venation to reduce water loss and dehydrating the cutting. Keep the cutting warm, in bright light, and out of the wind until it roots. When the cutting is pushing new growth, you can start to fertilize. You can do this anytime, but summer is best. People in more northerly climes would want to propagate in July. No rooting hormone is necessary - it will root easily as long as you keep the soil moist and don't drown the cutting by having the cut end in soil that is saturated.

Al