A reasonably detailed Wikipedia biography of Mitchell is here. It notes that she spent two years at Smith, a Seven Sisters college (the Ivy League equivalent for women in times past), then studied at the Art Institute of Chicago where she earned BFA and MFA degrees. It also mentions that her health was poor for about ten years before she died. Not much touched-on was that she was very difficult to get along with, though that's irrelevant regarding her art which was Abstract Expressionist, having no intrinsic meaning or message.
Below are some images of Mitchell's paintings that I grabbed off the Internet. I'll use them to help explain why I think she was a lousy artist.
She was of the "action painter" variety of Abstract Expressionism, where brushwork is the featured component of the painting. Seen here are several works that are large, have essentially white backgrounds, and use a similar set of other colors. I imagine that she could crank out an average of at least one of these a day.
This was done the year after she got her MFA degree, It shows a bit of compositional structure, unlike most of her later work.
This too exhibits some structure -- in the form of pseudo-Cloisonnist (or Cubist?) light-colored segments offset by a tangle of other colors
An "action" painting lacking the kind of purposeful or structured action paint strokes of, say, Franz Kline. Mitchell is doing little more than simply smearing paint.
She spent much of her career in France, hence the "dirty snow" title.
Like the previous painting, Mitchell at least uses colors to roughly establish zones for her consistently agitated brushwork that seems to have featured shorter strokes as her career progressed.
Painted when her health began to worsen. Like "Buckwheat," she uses essentially opposing colors, here with the little white and black and a touch of red to make the effect less relentless.
So far as I'm concerned, Mitchell's greatest defect is that her paintings are not very interesting. Her color choices are often poor, though Sale neige and Buckwheat show some spark. Her "action" brushwork strikes me as little more than dithering. As for composition, often enough it's a matter of placing a blob of increasingly dense dithering towards the center of the canvas.