At the core of the Buteyko method is a series of reduced-breathing exercises that focus on nasal-breathing, breath-holding and relaxation.
Two of the three focuses of the method are not applicable to divers...
It seems to me that all 3 are applicable to divers 90+% of the time. They just aren't applicable while diving. I thought the point was not that you do those things while diving. The point was that you do those things as part of some training regimen and the results would benefit your diving (and other things).
I.e. if you practice breath-holding, it seems like that might gradually help you to breathe more slowly. And if you practice nasal breathing (and that helps reduce airway inflammation as the Buteyko people claim), then when you get in the water, you'll still have more open airways to benefit from, even though you're breathing through your mouth.