I saw an in depth interview with the guy that was caught in the canyon. He didn't "just" cut is arm off. After 3 days, he realized what he had to do but only had a blunt pocket knife. So first he had to sharpen the knife on the rock. He then had to break both the bones in his arm so he wouldn't have to cut through them with his crappy little knife. Then he cut through his arm where the bones were broken. I believe it was quite a long hike back to his car after that.
Humans are capable of insane things when really pushed if they have the will to survive.
In this situation however you have to laugh at the stupid redneck. While he probably couldn't cut through the handcuffs, why would you cut off your hand when the handcuffs were only attached to a slim rod of rusty looking metal...ROFL. Just carry the damn handcuff around your wrist till you can get it off at a later time!