Hacked off is normally a phrase used with negative connotations. It is normally used to infer that someone is unhappy, annoyed, or irritated, especially because of a situation that they find themselves in.
He was really hacked off when they lost the game.
She’s getting a little hacked off with all the travelling she has to do.
In this example when you hack something off (in this case the womans hair) it means it has been cut off with strong, rough strokes normally using a sharp tool or implement, such as an axe or a knife. so not evenly or neatly.
Kim hacked off her long hair.