Try using a reverse drill bit or an easy out . If it was a recent break it may come out easily and you won't have to do the next steps . Re-torque all the rear end bolts .
I noticed one of the gators had a small puddle under the rear end . When I checked closely I saw the bolts had backed off a little and one was actually snapped off in the rear end . Not uncommon to see rear axles loosening off and axle seals leaking . If you just finished a project on the course and had to use carts to run lots of material then I would suggest to take a look in this area and snug things up afterwards .
Pretty easy repair . I removed the battery cables and key before starting . Just in case I have to do any welding . Support the frame and rear end separately .
Remove the pin for the brakes and loosen off the 3/4 nut on cable . Pull the cable through and out of the way . Remove the three bolts holding axle to frame . 2 up top on pick and 1 inside bottom .
Next remove the axle to rear end bolts . Axle just easily pulls out . Check the inner seal in rear end .Replace it if it's damaged .
Now the broken stud is easily accessible . You could weld a nut on it and remove or...
try the vice grips first . Most of the time they come out this way . They are usually loose .
Before installing the axle clean everything up well and I put a little rtv sealer here before installing . Be careful that you don't tear the inner seal with axle .
In this case torque bolts to 35 ft lbs ( axle to rear end). Always torque bolts half the amount first in a criss cross pattern . Reassemble the rest in reverse order .Wheel nuts 65 ft lbs. Check the fluid and top up if needed . Only took < 1 hr. taking my time .