A year ago a m/b graft here did the same thing, and I let it grow so as to get a quick sample of what kind of fruit the scion would produce. It was really a poor tasting but big-enough berry. I hoped that a year of additional growing would p o s s I b l y p o s s I b l y give the scion a chance to "be all that it could be". Well, the added year of growth resulted in more of the same exact berries. You lose some, you lose some.

It's very demanding on many fruits to bear on new scions too soon, and can set the growth of the scion back badly- but I can't speak to mulberries specifically. On my apple and pear trees I automatically pinch these off.