this topic really just irritates me. Why people are still performing surgery on their tubes is beyond me. Y'all are doing WAY more work than you need to.
Just take out the plastic insert. That's all. Its what is put in tubes like this (like mascara, lip gloss tubes) to suck excess product off the wand so you don't end up with a globby mess when you remove the wand from the tube. If you've ever gotten a tube of mascara or lipgloss that was missing one of these due to a manufacturer mistake, you'll know what a mess you have when you don't have that insert in there.
When you get to the point where you think your tube is DEAD, just remove the insert. You'll get much more product on the wand (not the doe tip, the actual shaft of the wand) and you can take it off with your finger or a brush. Your UDPP won't dry up this way either, as it does when you try to transfer it to a jar.
Although, if you still want to go through all that nonsense to cut your tube apart, that's your crazy choice. You just don't have to.