Disney couldn't come up with a better villain. This is a woman who literally is jealous and resentful of a nine-year-old girl because (1) she speaks better French than her and (2) doesn't act scared of her. A real winner, right?
Check out Sara's first impression of Miss Minchin:
She was very like her house, Sara felt: tall and dull, and respectable and ugly. She had large, cold fishy eyes, and a large, cold, fishy smile. (1.25)
Yuck, right? No wonder she gives Sara a bad, bad feeling. And it turns out that, at least in this case, you can judge a book by its cover: Miss Minchin is mean-spirited, ungenerous, and really, really cruel to orphans. This is how she breaks the news of Sara's father's death to her:
"You will have no time for dolls in the future," she said. "You will have to work and improve yourself and make yourself useful." (7.162)
Miss Minchin is the kind of person who lacks all compassion and only cares about money and appearances. In fact, the only reason she agrees to keep Sara after she's lost all her money is because the lawyer says it might look bad to other people if she kicked a little girl out on the street.
And she realizes that she "could not afford to do a thing which would make people speak of her as cruel and hard-hearted" (7.107). Notice that word "afford"? That means that Miss Minchin cares about money. She doesn't want to lose students by looking cruel—but she sure doesn't mind being cruel in private.
In the end? Miss Minchin gets her just desserts. And we're pretty happy about that.