It sounds like the chicken is dying, but it's not. It's like getting your nails clipped.
These were given to us by a friend of ours that doesn't really interact with chickens much, so they aren't acclimated to human touch. These particular chickens (3 of them) weren't getting along with one of their roosters, so he gave them go us. They're pretty wild, so I wanted to clip their wing feathers to keep them from flying.