Tinnitus is a symptom, not a disease and the causes may be in the cochlear in the auditory nerve itself or in the brain.
If the cause is in the brain then treatment surgical or otherwise is not acceptable.
If the cause is in the cochlear, then destroying the cochlear would make one "stone deaf"
If the cause is in the nerve....... acoustic neuroma....the removing the tumour "might" ease the tinnitus, but this tumour is a rare cause of tinnitus.
One could cut the nerve from the inner ear, the Acoustic Nerve...but that is not an easy procedure and would destroy all hearing as well
ABerrant gives an interesting link which is still in animal studies....but in humans, stimulating the vagus nerve would slow down the heart rate which would be dangerous in the over 60´s, the commonest group to get tinnitus.