First off, trying switching bearings before trying an axle ‘surgery’. Axles are easy to damage and trying to forcibly remove one should be a last resort. You may also want to try out checking every inch of the yoyo for any stuck objects, excessive dust, loose parts, etc.
Now, if that didn’t fix it, you may want to try to remove the axle. First, wrap a thick rubber band around the axle A LOT. Seriously. You did it wrong it wrong the first time you tried, do it again and wrap it around more. Make sure it’s TIGHT.
Next, try to find a vice grip, or at least a pair of pliers with a lot of leverage (but you’d be better off with a vice grip). Then, tighten it up but not too much. Try to rotate the yoyo. If you can rotate the yoyo without the axle coming out, just stop. You’ll probably strip the axle.
If worst comes to worse, you may have to pick up a new axle. They aren’t too hard to find. You can pm Calibuddah on the other site and he should be able to hook you up with one.
To remove the axle 100% of the time, throw it in a vice grip and tighten it as much as possible. Then, twist the yoyo. should come out no problem, but this will completely ruin the axle.