Beyond help means that any attempt to help will be futile: nothing that can be done will make the situation any better.
John is beyond help: he insists on doing things his own way, and ignores our advice.
Kathy has gone too far this time. She's beyond help, and will have to find her own way through this.
Helpless is an odd word; it doesn't mean "lacking help"† but is used today mostly in the sense of being incapable of acting on one's own behalf. Beyond helpless represents a common colloquial use of beyond to mean transcending: a person who is beyond helpless is so helpless, so incapable of action, that the word helpless is inadequate:
Sara's pretty helpless, she can't write the simplest email without making spelling mistakes or sending it to the wrong person. But Mike's beyond helpless: he can't even turn the computer on.
†The word arose at a time when help was used more often than it is today to designate resources or means of doing something.