Yes, they can be grown from a cutting like AlanKHart mentioned.
One thing however is that a lot of the times the
plant may return to its natural state. The lacy leaves on the Jap maples are a common abnormality. If you look closely at just about all Jap maples, there will be a graft, where the abnormal
plant tissue was attached to a normal trunk. Usually the grafted area has been turned upside down as well, creating the weeping effect.
I have seen where some
plants have had the normal wide lobed leaves on one side and the very delicate lacy leaves on the other.
Which can make a very interesting
plant itself.