You can take cuttings in august or september, take 4-6" cuttings of non flowering shoots, put them in a 50/50 mix of peat and sand, or a proprietary cutting compost, and ideally put in a propagator with a bottom heat of 55- 61 deg f {although they can be rooted in a cold frame}
when they,re rooted, pot them up into 31/2" pots and overwinter them in a cold frame, in april or may next year, plant them out in a nursery bed, grow on until planting them out in the autumn. derekm

Yes you can grow from cuttings. You can do it now. Take them from a non-flowering stem, if there is one.

Thank you Derek and Ojibway.

Given this is a new small hydrangea you might want to wait until next year before you take any cuttings and allow the shrub to establish itself.

Oh right, thanks for the info MG.