How can I create an excerpt for each of a node's taxonomy terms?
This is an interesting feature. I have never seen a  module which does it. 

If you look at the Open Calais module, you can see some custom extensions to the way taxonomy works. While it doesn't do what you want precisely it may be a  good guide for you. 

In short, you can assign meta data to a node-term relationship which contains your excerpt. It would require a custom module and a fair amount of coding.