If the stitches will dissolve on their own and will not have to be removed, then they are not a barrier to immersion in the mikveh. But if the stitches are the type that will have to be removed, then they are generally considered a barrier to immersion and you would need to delay mikveh. Check in advance with the oral surgeon – it is usually possible to arrange for stitches that dissolve.
If you can avoid it, you should not have the surgery immediately before immersion. Some dressing may have to be left in your mouth for a few days, and this would present a problem for mikveh use.
Other than the stitches, we can think of no medical or halachic reason why such surgery should not be done while you are a niddah.