For example, I have a post that's filed under category 1 and category 2. When someone clicks on it from category 2, I want to know the slug for category 2. If it links from the category 1 page, I want to know the category 1 slug.
Is this even possible?
As anything that has to do with stats this is really an analytics task and as such not something that WP does natively.
You options are:
installing (if not already) some kind of analytics solution and getting data from it
add code to that post that will track referers (I won't really recommend this since it comes with performance issues and poor caching compatibility)
