You don't say whether it's a gas or diesel engine, but I suspect the procedure is about the same.
I have done the clutches and belt on the 4010 Trans Diesel.
Yes, you will want to pull the shock and the exhaust. You will not be able to get the outer and inner covers removed all the way otherwise (well, you might get the outer cover off, but not having the shock in the way makes it a LOT easier to remove). The shock is only two bolts, the exhaust (at least for the diesel) is 4 nuts on the manifold and 3 bolts on the muffler. There should be enough room to maneuver the exhaust to remove it. For the diesel, you do not have to separate the muffler from the pipe.
I pretty much follow the manual, except I remove the bed for easier access.
Even with the shock removed, you will have issues getting the inner cover to clear the upper shock mount. It will come out, but you may have to bend the inner cover slightly.
The belt
can be changed without removing the clutches, but removing them makes it easier and you can damage the belt if you don't remove them, so use caution. There are special tools for removing the clutches. One holds the driven (rear) clutch while the center bolt is undone. One holds the drive clutch while the center bolt is undone. And one tool is the drive clutch puller. It looks like a long bolt. The center bolts should be about 70 ft/lb tight, so you should be able to hold the clutch by hand if you have an impact wrench to undo them. A strap wrench would probably work as well. But you might need the drive clutch puller.
The tools are pricey for what they are, but they do make it really nice when working on the clutches and belts. If you're going to keep the Mule for a while and do your own work on it, it may be a good investment.
I have repaired the converters on 3 different 4010's over the last couple of months, the last one also needed a rear main oil seal done. Which of course requires the entire converter to be pulled. In addition to removing everything for doing the clutches, you have to separate the spring from the axle housing and are supposed to drop the spring. It can be done without dropping the spring, but it's tight....
If you do remove the clutches, be sure to torque everything to spec and to use a medium strength thread locker. Also, make sure the rubber seals are in place correctly on the covers. I usually pull them out of the cover and put them on the tongue side first. When you look at how they go together, you'll understand what I'm saying.
Good luck!
NV