What happens if they hit a vein while piercing your tongue?

If the piercer hits a vein (this would be due to an error on the piercers part, lack of attention to what he/she is doing) the piercing will seep blood. This is not a good thing but much better than the piercer hitting and artery which will pump blood with little sign of it stopping. This generally require a trip to the hospital to have the piercing cauterized to stop the bleeding. So before you run into issues find a good professional piercer and do your research!!