FIDIC: With regards to procurement legislation, what is the difference between an 'Extenuating' and 'Mitigating' circumstances..?

The use of these two words are saying the same thing. You have an extenuating and mitigating excuse as to why you had to do something in a particular way.

In procurement that could be due to an emergency event, health and safety risk, public safety risk perhaps even a force majeure type event (something outside of your control).

A compellingn and defendable reason why you had to do it the way you did.