On all taper fit ball joint applications use an aluminum plate on the stud end and give it a rap with a hammer along the axis of the stud. Do not damage the threads, and do not use a pickle fork!!!!\
It is also possible to use a gear puller if you can get it in there, but be carfull not to damage the boot seals, these are expensive. You may want to put some penetrating oil on the joint 30 min. prior to the removal, but do not get it on the boot seal. Neoprene does not like oils.
On reinstalation clean the tapers so there is no oil. The oil will increase the pull up in the boss of the stud and increase the stress in the boss material.