I know nothing about Mules but I did have a gator which used a Kawasaki motor and a Tufftorq transmission.
On the Gator you don't need any tools or any disassembly. With the trans in neutral rotate the rear pulley by hand while 'rolling' the belt off the rear pulley. Roll it off to the outside away from the trans. Then you can wiggle the belt around and off the front pulley. The belts have arrows so make sure you put the new one on the right way.
You should also inspect the wear buttons on the rear pulley.
If you have to leave the unit outside where it might get stolen removing the belt is one way to make it harder to steal.