Our best luck with rooting mulberries is to wrap in a damp paper towel and bag loosely. Remove most of the leaves to limit water loss.
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That poor mulberry is in need of some roots, so first thing would be to get some rooting powder or rooting solution and saturate some paper towels, then wring them out lightly as you press them around the basal part of the trunk. As R Scott recommended, put the tree, wrapped at the basal area with those rooting solution soaked paper towels, in a large baggie and close the top of the baggie with either some string or twist tie. Don't make the baggie tight against the trunk but rather leave it a little loose, set this in a wide mouthed jar (like a Mason Jar) so it will stand up. pluck each branch down to only one or two leaves then place in an area where it will get sun and shade. Keep an eye on the dampness of the paper towels you want them moist but not dripping, in about three weeks you should begin to see new leaves budding.
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