The act of frequently shitting copious amounts of feces.
After eating an entire canister of raisins Joseph proceeded to shit like a mongoose the next day.
Comes from the way a mongoose moves – they're known for their fast, darting movements. So, "shitting like a mongoose" might be a humorous way to describe someone rushing to the toilet with urgency.
I ate a bunch of fiber and now I've been shitting like a mongoose all day.