You don't have to be a mortal to use a mortal stunt. They're called "mortal stunts" because anyone, including mortals, can use them. Why would you need a separate stunt affecting powers (e.g. Claws) when the character has already bought a stunt that affects his use of the skill they're based on (e.g. Killer Blow affects the use of Fists)?
You're confusing "neccessary" and "sufficient". That is, being a mere mortal is sufficient excuse to buy a stunt, but it is not neccessary to be a Pure Mortal to buy them.
Claws is a power that affects attacks using Fists. Any stunt that affects Fists can apply to Claws attacks, including Killer Blow. Any 'stunt' that modifies the way Claws work would be a power, not a stunt. This is why Venomous for Claws is not a stunt. Or, if you prefer -1 refresh power enhances, this is why Additional Emotion, At Range, and Lasting Emotion are listed as powers dependent on Incite Emotion, rather than as stunts.
I guess I'm at a loss to understand why there is so much controversy here, given that the dividing line between stunts and powers is really one of the most clearly worded things in the rulebook.