You won't need any special tools to replace the mandrel shaft. An impact driver makes the nut on the pulley and the bolt that holds the blade much easier to remove.
To remove the nut that holds the pulley on the shaft place a piece of wood inside the deck to jam the blade while you unscrew it.
You would be better off to remove the deck from the tractor before repairing the mandrel. The instructions for removing the deck are in the owners manual. You can download, view, or print a copy of the owners manual free at [managemylife.com
Use the block of wood to jam the blade again and remove the bolt that holds the blade on.
Start the nut that holds the pulley on the shaft 2-3 threads and drive the shaft down and out of the mandrel. You will damage the shaft when you drive it out and the bottom bearing might come out with the shaft.
With the shaft removed you can drive the bearings out of the mandrel with a long screwdriver or shaft. You should replace the bearings when you replace the shaft.
Drive the top bearing into the mandrel housing from the top with a piece of wood or a socket that fits the bearing. Put the bottom bearing on the shaft and pull it into the mandrel housing by tightening the pulley nut.
You can buy a complete mandrel by ordering part number 143651. The cost is around $70.00. The new mandrel has a new shaft and bearings in it. You have to reuse the old pulley.
I hope this helps.