What happens if you cut that little piece of skin under your tongue?

Likely nothing: The tag beneath your tongue is called a frenulum. In people (adults and children) with a prominent frenulum, they often have tongue tie and may require the frenulum to be cut (frenulectomy) so that they can have better mobility of the tongue. It is a painless procedure and rarely there is much bleeding. Babies typically have their frenulum cut without anesthesia and do well.