Some cutscenes will pause the game once they are triggered like when you open a chest, activate a shrine or clear a monster room. However when you pause the game before the cutscene triggers you can unpause it while it plays and move immediately. When you open the pause menu before the cutscene plays it will stay open and you are able to move with it. And when you opened up the pause menu and are able to move you can open a chest, unpause and move immediately.
Im not very good at explaining this so I made a quick video! (Sorry, I have no capture card yet!)
The ingame timer does not always freeze but at some moments it will. And there are also things I have not tried yet like using a teleporter in the glitched state.