It is easy for a dog to get a laceration in its mouth. Dogs frequently chew on all kinds of things, some of which can cut them. Dog fights and accidental lip/tongue biting can also cause lacerations. Whatever the cause, mouth lacerations are difficult to treat because of their location, but you can help your dog by keeping its cut clean and monitoring it for infection and further damage.
Hold pressure on a laceration that is actively bleeding. Continue to apply pressure until the bleeding stops. Use a soft, absorbent cloth such as an old washcloth or piece of toweling. Make sure it is as clean as possible so that you don't introduce dirt or germs into the wound. If the bleeding is from the tongue you will find it difficult if not impossible to apply direct pressure, so you may just have to let it bleed.
Take your dog to a veterinarian if the cut continues to bleed a great deal after 10 to 15 minutes. A mouth wound, especially a cut on the tongue, will often bleed a lot without being serious, but the bleeding will normally taper off and stop on its own within a short time. If the bleeding seems excessive or if it doesn't slow down and stop, the dog may need stitches and should be seen by a veterinarian immediately.
Feed your dog soft foods while its mouth heals. Hard, dry food may irritate the laceration and prevent it from healing. Also keep bones, sticks and any other hard or potentially damaging objects away from your pet while during the period after a wound.
Gently rinse the injured area with plain water once or twice per day to remove food particles that may be clinging to the edges of the cut. This is a good chance to examine the injury and make sure it is healing properly.