She does bad things, worse things.

Dumbledore has let the school fall to ruin; students petrified, murderers on the loose, a student even killed last year - it doesn't bear to think about.
Students have been horrendously bullied in classes, exposed to dangers and worst of all, not sufficiently educated in certain subjects to the standard they should be achieving. It's disgraceful, and yet everyone says Hogwarts is the greatest school there is.

She is doing it for the benefit of everyone, this process which she has come to think of as weeding.
Some might think dandelions are pretty, but they are weeds nonetheless and they need to be exterminated. This is her job, and she does it well.
She imagines Hogwarts as a garden. It is dark and twisted now but she will crack open the skylight and let in the pure air in, clean out the rot and cultivate a garden with discipline and management.
Weeds need to be destroyed, and flowers need to be segregated to grow better. The occasional leaf will need sniping, for the the good of the plant, even if it doesn't understand that, and she understands that.

It wasn't always like this. For a period everything was glorious: she was the Senior Undersecretary to the Minister, and a member of Wizengamot, and if Hogwarts had fallen into a state of neglect, it was far from her world, that little empire she had carved out for herself, and it did not bother her.

Then Cornelius came to her, and began to talk. He said what a valuable asset she was, how efficient and determined, and even ruthless.
Well. We do not know. We can only contemplate, but these do seem like the things he would say to make her feel like she was irreplaceable, needed, brilliant.
He told her about Hogwarts, how it had fallen into a state of disrepair, not only the building itself but the teachers and students too. He tells her this in a way that says that she could change this, she could make it so much better, but only her.
You would have power, he tells her, Defence against the Dark Arts teacher, eventually the High Inquisitor, -and he may have even dared to float the idea of Headmistress- and most importantly, they would respect her.

She agrees, elated on self-righteousness, determination and fierce pride- we presume anyway.
But now she is here, and it has not been quite what you imagined. She is utterly alone, save for the Daily Prophet in the mornings, like a friend from home, and constant owls to Cornelius, some kind of link between her and the world she once knew.
She wants to do this well. It cannot be a waste of her time, she cannot let all of this work go to rot, everything she has hoped for disapparate.
She will have to discipline these halls.

The plan is that by teaching basic defensive theory as opposed to more practical work, she and the Ministry hope to decrease the hold that Dumbledore has over his students, and educate them formally, and not on whatever whim takes her.

Admittedly, she is ruthless, but she is never cruel. Cruelty causes pain and suffering, and no one is suffering here. Are safer classrooms a hardship, and does making sure that teachers are competent cause undue distress?
Yes, it could be argued that her punishments are brutal, but she wouldn't agree. Take Potter for instance, that highly aggressive young man who constantly undermines her work.
The boy has shown severe behavioural problems throughout the years; misdemeanours include stealing, open defiance of basic magical laws, an unprovoked attack on his aunt, implication in the return of a mass-murderer, and presence at the tragic death of an exemplary student.

He needs to be dealt with. She has many approaches that she could use, but it would be fruitless to attempt to convince him that his fervour and passion are misplaced, that his pride in Dumbledore is wasted and his righteousness frivolous. He has anger inside him and he will not listen.

The Ministry explicitly states that Lord Voldemort had not returned and that Harry Potter's claims are only to garner attention for himself.
What proof does the boy have, she asks herself.
He states that Cedric died at Peter Pettrigrew's hand; the same man who was killed years ago. He claims that the Dark Lord duelled him, but the echoes of his dead parents distracted He Who Must Not Be Named while he escaped.
She does not need to explain why this story is not quite credible.

The boy repeatedly lies. He says the Dark Lord sprouted from the back of a teacher's head, a likely story. He says that Sirius Black is innocent, his mass-murdering godfather.
He says that He Who Must Not be Named is back, in an attempt to draw the limelight back upon himself by resurrecting his old enemy.
She has read his file, the young Mr Potter. Orphaned at a young age, troubled upbringing, textbook stuff.

How else then do we deal with weeds if they will not listen?
Well, if they are choking everyone else, jeopardising the garden, then we deal with them swiftly and with force.
The Minister agrees with this approach, and she would rather listen to the highest figure of authority rather than the ramblings of an old man who can barely run his school anymore.

And so she deals with the problematic student, because he must be taught not to tell lies.