Answer: Weeping mulberries are grafted onto an upright trunk of a normal upright mulberry. The upright shoots you see are most likely coming from below the graft union and should be cut off flush to where they attach to the main stem to maintain a weeping top on the plant. Mulberry trees are typically pruned during their dormant season (before they leaf out in the spring). I'd prune it now, even though it is technically early spring. Pruning now will encourage additional growth for this year. Mulberry trees take well to severe pruning so you should be able to remove all the errant branches without harming your tree. Best wishes with your landscape!
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