I heard that during Beast, if you don't perform well enough, you can even get kicked out of the Academy. Is that true?
Well, it is not as if some upperclassman can, on his own individual authority, decide to end a new cadet's career after a couple weeks. However, someone who repeatedly fails to perform to the minimal acceptable standards will be separated from the academy and, yes, that
can happen during Beast if someone demonstrates a complete inability to adapt to the military life and becomes a significant disciplinary problem and/or simply refuses to put forth a reasonable effort during his initial military training.
This is, after all, a service academy with a mission that goes far beyond providing an education to a student body. A cadet can "fail" out physically or militarily, not just academically. Since the initial military training precedes the first academic instruction by several weeks, it is not impossible for a new cadet to be told to pack his bags before he ever sets foot in a classroom. It is not a common occurrence, but it happens occasionally.
That being said, if a new cadet is
trying, a single failure will not result in separation. He will be given ample additional opportunities to succeed. Furthermore, before a cadet is separated, there are checks and balances within the system. His chain of command (both cadet and commissioned officer) will ensure that every effort has been made to help this individual succeed. It is usually only after all other reasonable options have been exhausted and it is apparent that additional efforts will not likely result in improved performance that separation will take place.