It has been my experience that when this happens, you most likely had the snap ring break on the end of the Clutch pack. If you pull the dipstick out and look into the transmission while in reverse, you will probably see or smell smoke.
It sounds like the clutch plates if forward are not releasing. So the transmission is actually try to go Forward and revere at the same time.
Seen this many times on trucks that got stuck in a hole or something and the operator tries to "Rock" it back and forth to get out. Will break the large Snap Ring on the End of the clutch pack.