The mad dog represents the anger and frustration you are suffering from. You should also expect some hardships while dealing with your business, because there are people who wish to make damage to you or your family. If you are able to run away from this mad dog, no worries, because you will overcome all the obstacles. If someone else have killed the dog that was attacking you, you will receive some support.
Dream dictionary: dog being killed dream meanings
…father died, and I dreamed one huge magpie flew in at the door and perched on one of the knobs at the foot of my bed, exactly a week before the death of my eldest son.”I, too, have dreamed of magpies, and, as in the case I have just quoted, the dreams have always occurred shortly before a death. The night a very near relative of mine died, I dreamed a large number of magpies flew in at my window; and the day before a dog to which I was very much attached was run over and killed, I dreamed two magpies settled on my shoulder, and that I could not make them go. Also, when I was living in a big, rambling house in Cornwall, I dreamed a raven flew down the chimney and pecked me vigorously three times on the hand. Indeed, the pecks hurt me so much…