In case it isn't clear, this stud is tapered, like a tie rod end. A tie rod puller can do it, as can the "poor man's" tie rod puller: try to put some leverage on the thing (a "pickle fork" might do it, or just a big lever in the right place), and then don't hit the threaded end of the stud, but take a biggish steel hammer and hit the side of the part the stud is inserted into (you're striking at 90 degrees from the direction of the stud, not trying to drive it out directly). If you can hit it hard enough and just right the stud will pop out. This will usually work even without any leverage on the part but it helps.
Never try to drive a tapered stud out by hammering on the threaded end. It will almost never work, and will mangle the end.