I have the same problem with my twins dd and ds
they are 2.10 we can't even do it when they are asleep, they wake up screaming!
Its the same when I have to trim ds hair! and its the same when we wash their hair!
Anybody would think world war 3 had started!
Onto a more positive note, I have a 10yo ds and he was the same, so don't worry it won't last forever, my eldest was ok when he hit the 4 yo barrier, then you could trim nails, go the the barbers, ok washing hair was a little harder, infact he still doesn't like it much but at least he doesn't sound as if your're murdering him!
Only consolation is, the twins nails do drop off, they peel them themselves and pass them to me. Toe nails are a bit harder, they arn't so soft, and can grow funny if you don't trim them!
We also use the word 'trim' instead of the word 'cut' a bit of reverse phsycology. To a toddler cutting nails is like you're going to hurt them, they don't understand cutting on this occasion doesn't hurt! so trimming, they don't quite understand, but realise it doesn't hurt!
All else fails, two people and torture time! I know they wriggle alot, we use 'clippers' but each to their own preference!
Was that gobbledigook or what, anyway hope I have helped!