the hair cutting-humiliation scene

I think it's because a lot of women like their hair.

It is indeed symbolic. There is an old belief that the soul resides in the hair. For example, when a woman decides to become a nun and enter a convent, her hair is cut as a sign that she is giving up part of herself, her individuality, to become someone who will only serve her god henceforth.

In the middle ages, when a woman was accused of being a witch by the inquisition, one of the first actions was that her head was shorn. It was a violation of her person, of her womanhood. In the German language, there is a saying to this day which goes "to get away unshorn" - meaning, to get away unharmed/intact.

In magical traditions, hair is often used as a substitute for the person. And throughout history, people have kept locks of hair of their beloved, or of a son or daughter, as a keepsake. Hair is a deeply personal substance.

If you cut out the hair of a prostitute and leave her looking horrible like in the movie, it's obvious that men will feel repulsion and clients won't approach her the same.
Even if she's not a prostitute, on a simple mob level, cutting the hair of a woman (like butcher it) makes her undesirable, makes her less of a woman, less than a human being.
That's the stereotype association: long hair=femininity.

They wanted to intimidate her, make her ashamed. She had beautiful hair and they wanted to intimidate her, and they did.