He tries to keep his private life and public life 'separate' (from each other). = He tries to keep his private life 'separate' from his public life.
('US') He fell and 'separated' [='dislocated'] his shoulder. [=caused the bone in his shoulder to move out of its proper position]
The competition has been easy to this point, but now it gets tough and we'll really begin to 'separate the men from the boys'.
(..) You alone are the food jamming mouth, aren't you? Enough! Food! Prepare for ice age! Protect the Dodo valley! Survivals separate the Dodo off the peak! Protect the Dodo valley! Prepare for ice age! Ice age? I've heard of these cracks, buddy. Intruders! (..)2002 Ice Age