I've never had to cut one off, I have the standard puller (similar to the Halfords in the pics) and it seems to work fine - but I use my impact wrench with a good black impact socket rather than a breaker bar.....sometimes they make a heck of a bang when they come off!
I also use differential gear oil on the threads of the puller bolt to keep them from seizing or stripping. It IS important to line it up properly so it's pulling straight off.
I made my own puller way back in the 60's, just a triangle shaped piece of 3/4" thick steel threaded in the center for a 1" bolt - crude looking, but it always worked a treat!
Edited by Magneto, 05 July 2019 - 06:16 PM.