Tissue tying the tongue to the floor of the mouth or mandible (jaw bone) is called a lingual frenulum.  The patient is often referred to as being tongue tied (ankyloglossia).  When the frenulum is tight and the motion of the tongue is restricted, especially if the patient's speech is affected, a frenulectomy may be recommended by your doctor.

Simply cutting the frenulum may result in partial recurrence.  Cutting the frenulum and stitching the defect will often give the best results.  General anesthesia is usually recommended since the patient needs to be still so the salivary gland ducts are not injured during surgery and if bleeding occurs it is easier to control.   
 

The Video below shows the division of a thick lingual frenulum with significant bleeding. 
This is why I do not perform this procedure in  the office.