There is no Biblical injunction against a woman cutting her hair. You are thinking of 1 Corinthians 11:6 where, in the context that the long hair of a woman is her "glory" and acts as a covering and symbol of her subjection to her husband, she is not to be "shorn” or "shaven”.
The word "shaven" is Strong's number G3587 ξυράω - xurao - and means to literally be shaved.
The word "shorn” is Strong’s number G2751 κείρω - keirō - and means to shear as in shearing a sheep.
The injunction is not against "cutting" the hair but against shaving the head to take away the hair completely. A haircut that is feminine and not designed to make a woman look manly or "butch", as they say in popular slang, does not violate any scriptural injunction.
1 Peter 3:3,4 Don't be concerned about the outward beauty of fancy hairstyles, expensive jewelry, or beautiful clothes. 4 You should clothe yourselves instead with the beauty that comes from within, the unfading beauty of a gentle and quiet spirit, which is so precious to God.
Peter's caution is to be preoccupied with Godly things and not to be overly concerned with outward fashion. He doesn't say anything about perming or shampoos etc. The main thing is that a woman's hair should be feminine and not masculine.
I hope you have found this helpful.