My Scag zero turn throws belts too. I think I've figure it out, but it's too early in the mowing season to be sure. It only happens when I first start to mow with it, but once it's been mowing for a while, it works properly.
New blades made it better, but didn't fix the problem.
I changed the type of grease that I was using on the spindles, and that helped, but it still happened. I bought new belts and that helped, but it still happened. I bought new springs that control the tension, and it hasn't happened since.
In my case, I think that everything was causing it, and by just replacing one thing, it got better, but it didn't completely solve the problem.
If it happens again, I'm thinking that I need to find a soft start switch to turn on the PTO. I don't even know if such a thing exists, but that's what I think I might need.