I would only use the gear puller if you wanted to get a new crankarm; since they bear on such a small area, they have a tendency to damage aluminum arms. They work great, but if you want to re-use it, try drill-chuck wedges, designed specifically not to damage the thing they are removing. A "pickle fork" style tie-rod remover works great as well, with lower incidence of damage to anything that matters, and can often be found for $10-12 at an auto parts store. The Hozan tool (the exact same thing, shorter!), since discontinued, would set you back 2-3x that!

Also, that's generously 1/2 engagement on that tool, based on where the thread is damaged. Depending on how tight of a fit there is between the original threads/the puller, it may be enough to remove it, but I wouldn't chance it. Bicycle Research makes a tool that many shops have (as the poster above said) to clean messed up threads.

FYI, if you're shooting for destructive removal, hacksaw/rotary tool a notch above the spindle eye and whack it with a cold chisel. Provided you have that stuff already, it's free and quick.