While mange itself is treatable and not typically fatal, if left untreated, it can lead to secondary conditions that are much more serious -- namely, infections that indeed can kill him. If your dog shows signs of mange such as hair loss, intense and frequent scratching, crusty and flaky skin, rash and other symptoms, take him to a vet as soon as possible to get him the treatment he needs.
Mange is a skin disease associated with mite infestations. As the mites burrow into your dogs skin, they multiply and feed, causing intense irritation and hair loss, typically starting around the ears. This is stressful and physically uncomfortable for your dog, who will feverishly scratch at the infestation site to the point of self-harm. This scratching and the infestation can cause your dog to develop skin infections, which can become serious and fatal if left untreated. Mange is treatable with medication, so if you suspect that your dog has developed the condition, take him to a vet for help before the irritation leads to infection. The vet will probably start a regimen of ivermectin.