Can Beat Cop be discarded during another player’s turn?
Yes. Any player can use free actions, like the Beat Cop's ability, during any player window, including during another player's turn.

From the rules reference.


  Free triggered abilities ([free action symbol (squiggle)] triggered ability  may be triggered as a player ability during any player window.


and


  The red boxes are player windows. Players may use [free action symbol] triggered abilities in these windows.


See pages 23 and 26 of the rules reference for the timing of the player windows.