You can try covering the roots with something in an attempt to get a crop this year, but you will have to have the tree removed if you can't get it upright and back in the ground. Taking hardwood cuttings is possible, but it won't be like the tree you've got now - plum trees are grafted onto other rootstocks to give them vigour, or to restrict their height and spread, depending which rootstock is used.

If the ground was so wet that the tree couldn't support its own weight, then I would re-site it. Water logged ground isn't beneficial for a plum tree and will cause problems. Maybe move the tree to higher ground?