Depends on how severe the cut is. Rinse well with an antiseptic solution and keep the pup licking up ice chips; but cuts less than an inch long don't have enough flesh to consider stitches. Hopefully it'll heal without getting infected.
How To Treat A Cut On Dogs Tongue?
The cut needs time to clot. The dogs clotting process will stop when he cools down. Watch the cut & if it bleeds for more that 1/2 hour you need to take it to the vet. The vet, depending on the size of the cut, will either cauterize with a laser to stop the bleeding or determine if stitches are needed. If stitches are needed the dog will need to go under for sutures.
If it is deep and long, take it to the vet. If it is shallow like a paper cut, its own saliva will heal it.