You probably need to properly support the pully from underneath and use a press. When you use a 3 jaw puller, most of the time in applications like this, you just bend the pully inward making it tighter on the shaft. In other words, you will "taco" that pully before you get it off using a 3 jaw puller.
Does the pully have threaded holes in the top? If it does, you can use studs threaded into those holes and a jack screw on the shaft to pull it off. Otherwise, alteast put a couple pieces of steel under the pully and use a shop press. A split ring on a shop press is best where you can support the pully 100% around it's diameter, that's if it's just press fit and there is nothing else holding it, of course.