This might be different depending on what platform you’re on, but on my Android phone I don’t need to exit the application to do this. I just quit before I fire off the first bird, press arena again and there’ll be a new opponent. I use this all the time because there’s little point for me of battling an opponent with a full lineup of lvl 8 birds and 13 cards.
Also you might have noticed that Rovio added computer generated opponents a couple weeks ago (as opposed to the recorded player opponents). They play really bad and are easy to identify so if you combine the two methods above you get a 8-10 star win every time (unless you make some big mistakes).