GC holder flying Europe from Mexico

[Shami]

Hello!
I guess my question is a little bit strange, but a friend of mine advised me to do that, so I need to know if it works.
What he told me is that if I fly Mexico to Europe, American immigration will have no record of me leaving USA. Of course, after that I need to come back the same way. I know that there is usually no check crossing the border to Mexico, but does that mean that they won't send info if I fly to Europe after that?
The thing is that I have spend 5months and 2 weeks this year outside US, but need to come back and graduate university in December. That's why I need a month again and I don't want to ask for a re-entry permit, because I will be applying for citizenship next year.
Please help with this issue? Is it worth trying? Or should I just wait and then do what I can do with education?

Thanks!

[knowledgeable]

Cheating~

You're trying to cheat the system. Almost committing fraud.

It's your funeral, man.

I can't even wish you good luck for this shocking escapade.

[PraetorianXI]

When you present your passport. They will see the mexico stamps and the europe stamps. And send you back to your country for good, all because of trying to lie/cheat to obtain immigration benefits.

Do not try that.