Yes. It is normal for cats to play with mice. And by that I mean playing with their food.
All the indoor/outdoor cats I've had while growing up would spend endless hours playing wtih a mouse and never killing it, unless we stopped them.
The cat has great fun, but it eventually exhausts and frightens the mouse to death - which is why whenever I see it happening I would interfere and make the cat stop. Either kill it or leave it alone, but don't spend an hour tormenting the poor thing!
They'd follow it around, get in it's path, put a paw on it, sniff it for ever until the poor thing died.