ist it possible to say
She has cut her hair or should I say
She has got her hair cut
I mean she hasn't cut it by herself.....
Not a teacher.
In American English, I believe "she's cut her hair" would widely be understood to mean "she's had her hair cut" (especially with proper context or without any reason to assume otherwise).
I would specifically say, "she's cut her own hair" or maybe "she cut her hair herself" if I wanted to convey that idea. (Or supply additional context clues: "She took a pair of scissors and cut her hair.")