It's used by the characters to express intense frustration or annoyance. It's a pretty common term in the book, especially among the Greasers.
Here are some examples:
* "Darrel's eyes went black and he looked like he was hacked off about something."
* "I was hacked off at myself for letting them get to me."
* "Ponyboy was hacked off at Johnny for getting into a fight."
So, when a character in "The Outsiders" says they're "hacked off," it means they're really, really mad!