I find it very distressing to witness the disfiguring of my grandaughter while my daughter says it is ok for her to cut her own her hair, from beautiful long curly hair to a hacked haircut. What can I do about this?
Assuming you're not your granddaughters legal guardian, remember that your granddaughter is not your daughter.
When a parent (read: any legal guardian) is present, knows what is going on and has okayed it, you are not to interfere. The only exceptions are when she is (in danger of) hurting herself, or hurting you or something of yours.
If those exceptions do not apply, leave it be, how hard that may be, and take it up with your daughter instead, in private.
Honestly, unless your daughter gave her a large sharp knife to cut her hair with, it's not abuse or anything. It sounds like your daughter is letting her daughter take some control over her own appearance. If, once she's done, your granddaughter is displeased with her haircut, take her to a hairdresser for a repair. If your granddaughter likes her hair, LET IT ALONE.
Else, if you find it distressing, I recommend you remove yourself from the situation (either physically, or by reading a book or otherwise distracting yourself).
The answers provided so far are a bit brusque, but I'd suggest that's because, as you most likely know, we all want to be free to raise our children in our own way -- sometimes quite different from how our parents raised us.
I remember telling my mother when I was rather young that I wasn't going to learn from all of her mistakes: I would sometimes make my own mistakes and learn from those and that is OK. (I've always been rather precocious, lol.)
To me, parenting isn't about controlling your child, but teaching them to think about choices, considering the positive and negative consquences and then letting them (where it isn't dangerous) make their own decisions. To that end, when my daughter at 12 wanted to dye her hair, I talked with her about the consequences to ensure she understood them, but ultimately let her make the decision to dye her hair... she now regrets it and "never" wants to dye her hair again.
As mentioned in one of the comments, a private conversation with your daughter to understand her rationale may be all that's needed for you to accept the parenting decision she has made. If her decision seems illogical, then it may behoove you to kindly offer a consideration of all the facts at hand for your daughter to re-evaluate her parenting methodology, but ultimately provided she doesn't allow or cause harm to her daughter, her choice of parenting is in her hands -- we don't always like or approve of the decisions our children make, but did our parents always approve of our decisions?
The perspective we have taken with our kids is that while we would love them to have great hair all the time, it is fun for them to mess with it, and it can help get it out of their systems.
We'd rather they did it now than when they are going to job interviews as adults, so we encourage them to do what they like - and this has included a bit of self haircutting, mohawks, colours etc. It's fun.
My parents maybe wouldn't have liked it, but it's only hair.
I'd suggest relaxing and realising it won't make your granddaughter a bad/ugly/crazy person, it doesn't make your daughter a bad person, and it definitely is not your business unless either of them wants to make it your business.
I happen to believe a parent's responsibility doesn't end when her children are grown, it just changes somewhat. Does it bother me when my Mom offers unsolicited advice about my own children? Sometimes yes, but I understand there are things I can and do still learn from her, that it's still part of her role, and that I am free to take what she says under advisement and still do it my way.
She is kind and wise enough to not undermine me in front of my children, to use a degree of tact in bringing things up, and to leave it alone after she's given her input. It sounds like you are extending that same courtesy to your daughter.
Understand there are things everyone likes and doesn't like about their own upbringing, and often parenting style is deliberately chosen to be different in certain areas from one's own parents. I'm sure you can think of things your mother did that you didn't want to continue to the next generation. Who knows, maybe one of those those things was even that your Mom never stopped you from making mistakes like hacking your hair! That's not necessarily a sign of disrespect. It's a sign that your daughter wants to learn both from your strengths and perceived weaknesses.
I would go with the Stephen Covey approach of "Seek first to understand, then to be understood." Have a conversation with your daughter about why she feels it is important to her to let her daughter cut her own hair. Listen completely before making any judgements. Once you fully understand her reasons, you might be surprised to find you actually agree. If you still disagree, you will have a better understanding of how to share that in a way she will understand.
A lot of parents are permissive because they don't want to stifle their child's creativity, but sometimes it's hard to recognize there is a middle ground where children can be creative without being destructive, or to recognize the difference between stifling and providing supportive structure and guidance.
There is middle ground between letting a four year-old cut her own hair and preventing a four year-old from having any say at all about her own body. A good compromise would be to let the daughter choose her own style, but get it cut by a professional so it turns out how she intended. I think it's a great role for a grandparent to suggest alternatives your daughter might not have considered, while taking her unique parenting style into account.