I believe that schools should discipline their students for cyberbullying and here's why:

Whilst cyberbullying can occur between strangers, the majority of it occurs between people who know each other, from work or school or anywhere else.  Now, the main argument against schools disciplining cyberbullies is that it doesn't occur in school and therefore is not the school's business but a matter for the parents. However, cyberbullying online can often spin off into bullying in school, especially if the cyberbully and the victim know each other, and it's required of schools to cover this bullying.  With the argument of it is the parent's problem, bullies aren't motivated to become bullies just because, they're usually motivated by an unhappy childhood or through rampant spoiling by their parents, which gives them the emotions or feeling of superiority, pick on those who show weakness, usually asking these parents to punish their child for their actions has proven ineffective.

 Cyberbullying has been proven to cause thoughts of self-harm and suicide and in a worryingly large amount of cases, they have actually committed suicide e.g. the suicide of Megan Meier. Various laws have been implemented in various American states to give power to schools to discipline kids that have cyberbullied, even if it wasn't technically at school.

This isn't really an issue about the very technical legality of it, it's about protecting children from having to suffer the misery of constant personal attacks against them. I am not saying, be overprotective, but in the end, no child deserves to be cyberbullied and if they are, then the bully needs to face justice and the victim deserves to feel safe again. 

I just don't think that most parents of bullies will discipline a child enough to end their horrible ways, maybe they will, but if they don't, we're putting the mental health of many children and teens on the line.

That's what I've got, for now, thank you for reading and have a good day!