Oh, I would not clip the soft tissue!
That has to be painful. If there is any hard nail or jagged edges, I would try to trim those carefully. Word of caution here, you may want some to help you hold the dog or muzzle.
I've treated broken nails at home but not one like you are describing. I would try to clean it with a little antiseptic, make sure it is dry, apply a little antibiotic ointment, cover with gauze and some Vet wrap. Put a sock over that if the dog won't leave it alone. Watch for swelling or the dog limping. Best to not let the dog lick it. You need to watch for infection.
I am not a Vet and, if it were me and the nail were damaged like that, I think I would have the Vet check it.