Normally this kind of problem is caused by something being jammed into the pulley. I have seen everything from gumballs to rocks stuck in pulleys. What this does is cause the belt to ride onto the debris. Because it's spinning very fast, when it spins the place where the object is, the belt is free to move up or down. That's when the belt comes off.
It is also a possibility that the input shaft on the transmission is worn allowing it to wobble. If that shaft is wobbling, the pulley that's mounted to it will also wobble. That has a very similar effect as debris being jammed in the pulley.
It is also possible that there is just a belt keeper that is out of place or missing. I do not recall how the belt keeper systems are set up on a John Deere and have no way to access a photo currently, but most systems are real close to each other. That being said, there is some form of a belt keeper on that rear pulley. If that belt keeper is not there or out of place, the belt can (and usually will) come right off.
Check those things and if they all look in order and the problem remains, re-submit your question with some more detail and hopefully we can get you back mowing again.