A. arguta cuttings are easy to root, just stick in water. A. chinensis and deliciosa are harder and I have not had much success at all with dormant cuttings. Green shoots are not too bad if you have a mist system, but not sure that just sticking them in the ground would work very well. I would suggest putting the green cuttings in water, and change the water every 3-4 days. Bubbling air into the water will also help keep the cuttings oxygenated. Keep them out of direct sunlight, but with good, indirect light. If you do get roots, you then have to transplant to soil under high humidity (under a dome, tent, etc.) and very gradually expose to air to harden off. Water rooted cuttings are very sensitive to shock if you go too fast.
I’m testing another method right now for rooting dormant A. chinensis cuttings. I placed cuttings upside down in damp sand in a bucket, and buried the bucket with only the top 2-3 inches (5-7 cm) exposed. The bases were dipped in rooting hormone. The sun warms the top of the sand (near the base of the cuttings), while the deeper sand stays cool and prevents the buds from breaking. It may take 3-4 months, but you should eventually get some roots. The cuttings can then be planted pointing up in soil. I started some in mid February and it looks like I may be getting some small roots starting to show up.