You can probably dig the thing out, trunk chop it, remove most of the roots (keep a few feeders if you can close in towards the trunk--these usually have a few thinner ropy roots that can be wound into a pot after collection), bareroot it of all soil (using a hose) and put it in a growing container with bonsai soil.
Chinese elm, like most elms, are very tough customers and vigorous. I don't think you will have any problem with re-rooting one of these that's been in the ground. It will have a lot of stored energy to push new growth with.