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]
(..) Hello, Lucy. How are you doing? Wow, looks like your date's out for the count. It's like she's been shot with a mild moose tranquilizer. Yeah, I'm winking because that's what actually happened. what's happening here? She no like? Oh, she's just, uh... (..)2013 Despicable Me 2