Q.Can I Grow Rose of Sharons From Cuttings?
How and when can I cut the stems of my Rose of Sharon to grow more plants?

Certified GKH Gardening Expert
I would say yes. Since Rose of Sharon shrubs are actually a variety of hardy hibiscus, cutting would be taken much the same way. They also self-seed when not deadheaded, so you just might find some seedling growing beneath the shrub, which you can easily pull and pot up or transplant elsewhere. These articles will help: https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-propagation.htm
https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm