If only a few branches of the weeping mulberry tree are blooming should i prune off the rest that sre not?

I bought the tree at a local bomgaars and it took quite a while for ANY growth to appear. Some of the branches are dead and can be snapped off,but when you lightly scratch the trunk, it is green. As well as on SOME of the branches.If only a few branches of the weeping mulberry tree are blooming should i prune off the rest that sre not?
Don't do any pruning at this time. Remove only the dead limbs. The leaves of a tree is what provides nice fruit. This is due to the osmosis occurring. It's the same for muscadine grapes. The more leaves you have, the sweeter and bigger the fruit. You will limit the fruiting wood for next year if you remove the non-bearing limbs. If you need to shape the tree for next year, wait until the tree is dormant in late winter/early spring. Never prune more then 1/3 of any tree at one time or in one year. This will set it back. I would only remove the branches that are rubbing against each other.