Never worked on your brand before. All the ball joints I have worked on you can do two things, use what they call a pickle fork or put the nut back on (so you don't damage the threads) and hit it with a hammer. The pickle fork is a wedge U shaped tool that you drive in below the ball joint mount. This will separate the two pieces. Most any auto part store will have them.
You can also buy a puller which clamps to the ball-joint and presses down on the bolt to push it through the pitman arm/draglink. Or some Autozone stores will lend you the tool to do the job, I believe that's the company, others may too. Also note how many turns out the ball joint takes to remove and screw in the new one the same amount to save having to align the wheels.
If you're not reinstalling it, a good whack with a hammer should dislodge the stud, if it is being reused, a puller is the best bet, as a pickle fork is likely to tear the dust boot
Smack it with two hammers. You can do the double tap (see video below) or use one hammer to back stop one side and hit the other side of the mounting bracket. It helps to use some rust penetrate before the smacking begins.