Hello vktaylor, the first thing that comes to mind is that what you describe sounds very much like tar spots on the leaves of your tree, see the attached pdf's, however tar spots are not normally a serious problem and really more of a visual problem than anything else. The best treatment like most fungal disorders of leaves is to ensure you burn all infected leaves raked up. I don't like using fungicides since they kill beneficial and pathogenic fungi alike, rather apply a dilute solution of seaweed extract and organic silica as a spray onto the leaves, stems and buds and as a soil drench.
The branch/limb that you removed was it dead or not?
Check the pictures or tar spot and see if it matches what you saw on your tree
tarspot.pdf Leaf diseases on ornimental trees.pdf