Most likely it does not have a Posi-Traction rear differential and it's not broken. You just need to get it out of the mud or at least the right rear tire out of the hole it dug. If the truck had Posi-Traction both wheels would drive. But a non posi will spin the wheel with least amount of traction. There is a technique for driving in the mud or snow with an open rear differential and one of the main things is to avoid any tire spin. In a Chevy it is difficult to master. In a Ford you can select Drive 2 and it will start from a stop in 2nd gear. It makes it difficult to spin the wheels. The Chevy will still start in 1st gear even with Drive 2 selected. Once the right tire digs a hole it becomes time for a tow or a jack and wood, rocks and dry dirt, or wait for dry weather and let the ground dry out.
Don't take anything apart. Just get it out of the mud.
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