Hello there!

In the photo you've submitted I did not notice any blackening on the remaining stems; but the mention of blackening on the stems you've pruned away may suggest a fungal issue. These cankers are caused by fungal pathogens (Botryosphaeria sp. and Diplodia sp.) and are rarely serious, but can lead to limb dieback. There are no effective chemical controls for this disease once diagnosed, so prune out and remove infected branches promptly, and that's pretty much the only thing you can do. Do not compost the affected branches.

Healthy plants are less susceptible to these diseases. We've been in drought recently, and proper watering is important for dogwoods, which have rather shallow root systems. Exceeding dryness and waterlogging both affect dogwood roots negatively. Sometimes, the droopy yellowing foliage is simply a result of watering too little or too much.