Stare them down... make them retract... like Wolverine's claws.
Was gonna say a circular saw, but you could be paying a small fortune to get it sharpened. Try ( is it nail) SNIPS?
Angle grinder !! :)
A roundhouse kick.
You should make a video. It would probably destroy whatever you kick though.
Hotgarnet and Valcrogation are right...soak the nails for 30 or so mins first..just like when you shave...you always wet the beard first before shaving right?!....
Don't bother cutting them, they eventually break off anyway.