Hydrangea serrata 'Blue Billow'

Robert, how do you cut lace-cup hydrangea?

How do you prune it or how to grow from cuttings?

Well,,,both :)))

Cuttings are easy, softwood or semi-hardwood cuttings in mix of peat and perlite. Use IBA rooting powder for faster results. Cuttings start growing roots as soon as a week. Keep cuttings shaded and misted until rooted.
Prune just like any hydrangea macrophylla/serrata. I just cut off any dead in the Spring (wait until it has started growing so you don't cut live buds though, some buds start growing later than others). You can also cut stems back immediately after flowering before new flower buds are set.

What is IBA rooting powder, please? :))

It's a rooting hormone, most of the rooting powders you see at garden centers and nurseries are 0.1% IBA which is perfect for rooting hydrangeas and many other easy to root plants. Some rooting hormones that are sold use NAA, I've had decent results with both but IBA is recommended for most plants. I think Miracle gro sells a standard IBA rooting powder. Unless you're propagating a lot of plants, it's probably all you'd need for cuttings.