When you say restart do you mean that it won't do anything when you turn the key, or it cranks but doesn't start. The difference can direct what direction to look for your problem.
Since it shutdown while mowing, did you remember to turn off the deck before attempting to start. The safety shutdown circuit is normally separate from the starting circuit. So I am wondering if you have had a major failure. Can you turn the engine over by hand,
Most engines have a rotating screen that you can put you hand on to turn the flywheel. I am just making sure it will turn a completer revolution before checking other things, Making sure it just died and not locked up.