Tire not spinning

Can you free spin the tires on the axel that failed? IF so then the ring and pinon in the differential are most likely broken. Since you did not post the make model and year, if this sounds like the problem then you have big tires or the unit was spinning the tires and they suddenly caught or the clutch was dumped too fast.

Sounds like the tire is separating or has an inside bubble you . Either way you should check on new tires

No, even a 4x4 will have only 1 wheel that will spin on each axle in this instance. It's called a floating differential. For stock vehicles with non locking differentials like you have, both cannot spin or have full power at the same time. Hard to explain on this, but picture your car making a hard right turn. Both front wheels would be spinning at different speeds because of the turn. The passenger side tire is spinning much slower than the drivers side tire, therefore if both were spinning at the same time, your tires would chirp and skip on the pavement which would eventually ruin your differential. In offroad applications, we WANT the differentials locked and turning at the same time with true 4x4. But in normal everyday vehicles, even standard stock 4x4's, only 1 tire will do the spinning per axle unless it has possitraction or full locked axle. Clear as snow?

it is a part in the rear of the car that allowed the rear tires to spin at a diffrent speed , you need that when you turn in your car as the inside tire ( of the turn ) well spin faster than the outside tire

The only way it will make a difference in tire wear is if you are constantly spinning the tires and wearing them prematurely. If you are just turning traction control off but not spinning the tires any more than before you will not have any more wear.

ok first check to see if you have a tire separation the tire will have a high spot in it you can jack up the car spin the tire if there is a tire separation you can see it as the tires spins this is the most likey cause...

Stop on a slippery surface or a dirt or gravel drive, and accelerate hard enough to spin your tires. If only the rear tires spin, you are not in 4x4. If all four tires spin, you have 4x4.

Tires need replaced- may have a few other problems. try this
-unplug the saw spin the saw by hand, does track down the middle of both tires? also look at your guides and backup bearings.
I would take off blade-back off all guides and bearings -clean off any build up on tires- replace blade. now spin wheel ( always spin with the blade going down) if its tracking good go ahead and adjust guides and bearings to specs and try again. most likely the back up bearings are out of adjustment. they should not spin unless you are feeding material and it seems like the bottom one may be your problem.
But never the less it sounds like new tires are needed.

Need ti find out why back tire don't spin, ABS light came on because the ABS computer did not detacte speed (mph) at rear wheel so it's thinking bad speed sensor.

some of them has a key that helps both tires spin but alot of riding mowers have only one tire spin but not all it could be in the gears it's self