The teeth correction is permissible if it is done to return it to its natural state, this is considered a treatment not adornment or beautification.
If cosmetic surgeries are done for health reasons, then it is permissible in Shariah, but if it is to beautify and adorn or for fraud or cheating, then it is prohibited.

Sheikh Faisal Mawlawy, the head of The European Council For Issuing and Research, said: “correcting the teeth for health reasons is permissible in Shariah, rather it might also be demanded”.
But if the correction is to beautify, then no problem as long as it doesn’t involve teeth thinning, and setting of the teeth (which is freezing between the teeth to create a space after it is already sealed) and as narrated by Muslim, the prophet (Peace be upon him) has cursed (one who reduces or measures the sides of the teeth and who requests for it to be done).

He also has cursed (women who spaces between their teeth for beautification, changing what Allah has created).

These two hadiths were related to women only, but the analogical deduction of men on women in this matter is a correct analogy. But other forms of correction are on the original verdict which is permissible.