Can a school suspend someone for bullying for something that happened outside of school?

Yah!

yeah a school can defiantly suspend someone for bullying for outside of school

Yes, if its know that you are a trouble maker than why would they want you in their school

Yes, schools can do that and yet I can't give you a legal reason why. For example, if a guy rapes a girl at a party and goes back to school on Monday, he could get the boot from school over that. Yet again, I don't know the legal reasons why. I just know this is legal.

Many schools are different some schools do that and some don't, But I think its possible

Where was the video taken? In school? If taken at an outside public place, it is fair for publication.

in my school, you can get suspended for doing something outside of school like fighting or posting videos such as your example if they find out...so i guess they are allowed to do that...

The school has a duty to protect the safety and the dignity of students. They can be sued, for millions, if they fail in that duty. For my part, I care a lot more about the right of a kid not to be bullied than about the rights of a bully. What would your postion be, if a bully hassled a kid from school at a shopping mall on a Saturday afternoon? The point is that the hassled kid would not feel safe or comfortable coming to school. The district is in the business of educating kids, not making sure that the rights of bullies are protected by technicalities.

Fair? I'd have to say yes. Going to public school is a privilege, not a right. The school has every right to protect its students from bullies or other dangerous people.