Well, "on his back" he's vulnerable and demeaned. It is a position of least respect, which you actually should NOT need to cut or dremel his nails.
Having one's nails done is stressful enough without adding being on his back. This is his response to the stress! I'm in agreement. He could even be hyperventillating. Can you try him on his side, instead? It might not disappear, but should lessen, as he calms himself.
When I first read the title of the thread I thought it would be about the little pig grunts my Cocker makes when he's happy or eating something yummy!
Oh well...that's what I get for jumping to a conclusion!