No, early May I not too late to prune your Mulberry tree so prune away. I am charmed that you asked about mulberry as I am in Italy this week and just learned about how mulberry fed the silk worms for the Italian production of silk - and the worms and the mulberry leaves were collected and cared for by the children of Italy to help supplement the family income back at the turn of the century.  So your mulberry pruning crumbs would come in handy should you run into some hungry silk worms. Keep growing, Marianne Binetti