Cuts of the tongue and insides of the cheeks are usually caused by accidentally biting oneself during eating. Cuts and bruises of the lips are usually caused by falls. A tear of the piece of tissue connecting the upper lip to the gum is very common and harmless.
Cuts in the mouth usually don't require stitches except for loose flaps of tissue or gaping wounds of the tongue. Small cuts and scrapes inside the mouth heal in 3 or 4 days. Infections of mouth injuries are rare.
Press the bleeding site against the teeth or jaw for 10 minutes. For bleeding from the tongue, try to squeeze the bleeding site with sterile gauze. If you don't have gauze, use a clean cloth. Once bleeding from inside the lip stops, don't pull the lip out again to look at it.
Put a piece of ice on the area that was injured as often as necessary. Give acetaminophen (Tylenol) or ibuprofen (Advil) for pain.
For a day or so, offer your child soft food. Avoid any salty or citrus foods that might sting. Keep food out of the wound by rinsing the area with warm water after meals.