@Kjr928 - That most likely is Acer palmatum, a dissected leaf cultivar. Japanese maple for short, or JM, this is one of the weeping forms. There are hundreds of Japanese maple cultivars, unless the neighbor knows which variety it is it would be impossible to guess with any certainty.
It is true as a general statement that dissected leaf JM tend to not root from cuttings very easily, but this is not an absolute. There are some dissected leaf JM that do indeed root as cuttings. Since you don't know the cultivar name, only way to find out is to try. In August take cuttings of wood that formed this year (semi-hardwood cuttings). Cut a branch or two off, chop them to shorter segments. Make your cuttings 4 to 6 nodes long. Keep track of top and bottom, in that the part that was originally closest to the trunk should be the part stuck into the media in the pot. Remove all but one or two leaves, cut the lobes of the leaves to leave half the original surface area if the leaves were larger than a quarter.
I have used pumice, perlite, sphagnum moss and peat moss as rooting media. I've used 100% sphagnum, which works well, but the long fibers are a problem to tease out of rooted plants a year or two later. Lately I have used a blend of perlite and peat moss, 1:1, with good results. Make sure the media is moist. If you start with dry peat moss it can be difficult to wet. Wet the peat at least a week before you need it. Stick your cuttings into a pot of media, then set the pot inside a large clear plastic bag, zip lock freezer bags are great. Then set this bag in a shady spot on your bench and forget about it. Make sure the bag stays out of direct sun. Just before autumn frost, open bag to check. Cuttings that still have leaves will likely root. They may or may not have rooted, but if they still have a leaf callus has formed which is the first step in forming roots. Remove any dead cuttings. Close bag back up. and set in an unheated garage or other location that stays warmer than outside but under 40 F. all winter. They can freeze but it is best to protect the cuttings from temps below +23 F. for the first winter. In spring you can open the bag and set out the cuttings in the shade and the ones that sprout leaves will be the ones that formed roots over the winter.
Even with JM maple varieties that are known to root from cuttings, seldom will you get 100% to root. Pro's are happy with better than 70%. For the simplified pot in a bag trick, if you get 50% to take you did great. Try this several years in a row. Just because one year did not work doesn't mean it will never work. Try it without rooting hormone once or twice. Then try it with a commercial rooting hormone. Read the instructions, too much rooting hormone can actually inhibit rooting, so follow directions. I frequently have success without the use of hormones, so try it either way.
Or you could learn the art of Grafting. And make a copy of this tree by grafting scion onto Japanese maple understock. - In the sub-forum Advanced Techniques there is a forum for Grafting & Propagation. Some of the threads are good tutorials. There are also several discussions of techniques for rooting cuttings that are more detailed than mine.
Have fun, give cuttings a try. You might get lucky.
My neighbor has some kind of gorgeous Japanese maple tree. I don't know what species it is but it has these beautiful, delicate, lacy leaves and a crazy, twisted trunk. It's about 6 feet tall and has these beautiful sweeping umbrella branches. 
. And that it's not a bonsai. It's a stick in a pot
