He is, 'to put it mildly', a demanding boss. [=he is a very demanding boss]
He's 'mildly' [='slightly, somewhat'] interested in politics.
She was upset, 'to put it mildly'. [=she was extremely upset]
(..) Claude Chirac is calling on a secure line. What happened. I was called out of a meeting. The President suffered a mild cerebral attack. He's at the hospital. You didn't mention it before. I just found out. He won't serve another term. Not today. (..)2016 Me Before You