Answer: Dogwoods pruning should be kept to an absolute minimum, but removing deadwood is a good idea. Early spring is the best time to prune, but you can remove those dead branches now.
Don't use wound sealers but do sterilize pruning tools in rubbing alchohol between cuts in case a canker disease is involved in the dieback.
To promote good health in your dogwood, give it a wide, mulched bed around the trunk. Avoid overwatering and "pushing" the plant with too much fertilizer. During summer droughts wet the soil deeply once a week or so. A coffee can makes a good sprinkler watering gauge. Water until you've caught 1" in the can.
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