The removal isn't painful at all really, the healing process might make it a bit sore, but if you take good care of it and apply ointment as prescribed and keep it as clean as possible, then it will heal in no time.
I had one removed from my back when I was about 12. The actual removal didn't hurt, but the needle to anesthetise the area hurt like hell. It felt like they were digging it around deep into my back. I'd assume the eye area would be quite different though.
I've come to terms with my moles lately. I have about 5 billion of them, so there's no point in having any more removed.
I had one taken off my shoulder because my bra strap kept getting caught on it. It was no big deal at all. I should remove more for saftey sakes. Although the doctor I went to the last time said they looked okay. Mind you the one before that said they looked funky and she wanted to hack them all off. Im like dude! you want to remove how many??? I should do it....if only for vanity sakes. But really, how much better is a big pink scar over a brown spot anyway?