European Golden Eagles trained by falconers can be specialists on roe deer and are able to kill grown roe deer male on their own. Even wild Golden Eagles sometimes (very rarely) take down adult roe deer in Slovakia. A weak female Sika deer in deep snow can apparently become a pray for Berkut, the largest Golden Eagle subspecies from Far East.
Eagles normaly get their hooks on head and on the front part of deer torso when they attack. They kill probably by punctuating the lungs and causing pneumotorax, I guess? I´ve watched trained eagles during hunts, but´ve never actually asked falconers about the exact technique. First body part an eagle normally starts to eat is throat - they torn out trachea, so that any roe deer that may be still alive when it falls dawn and the bird gets its beak there is lost.