I agree with a pathogen as almost certainly being the cause. Trees tend to quickly wall off/compartmentalize injuries (wounds) very quickly. Dr Alex Shigo, an amazing man, devoted much of his life to gaining an understanding of the more obscure goings on with regard to how trees respond to our ministrations and their environment, and particularly how they respond to injury, like pruning cuts. It's possible that the pruning provided a pathway for the pathogen, but unlikely the pruning had any direct effect on the die back.
Some saprophitic bacterial infections like Pseudomonas produce toxins that can cause dieback of branches and even entire trees. If there happens to be any orange or radish lesions or pustules on the mulberry or any nearby trees, coral spot is another fungal affliction that causes dieback of branches.
I would prune off any branches that seem affected, especially if they show signs of a leaf spot disease, and hope for the best. Your cooperative extension agent, or perhaps a GOOD nurseryman might be of some aid if you are concerned enough. Suggestion: Clip a branch & put it in a Ziploc bag as a containment mechanism, and take it to any nursery so the nurseryman recognizes your respect for the health of his trees.
Al