Something I Cannot Stand

I am an easy-going person who takes almost everything with a sense of humor. This is why I get on well with many.  people, but However, there is a kind of people that are those whom I really cannot really stand. They are the ones people who bothers bully and harasses the weak people because as they know they are not going to defend themselves and this makes me sick. [Though this sentence is grammatically correct, it is ambiguous.  Do you mean you hate the bullies? Or is it the weak? Since they don't fight back!  Break it into simpler sentences and clarify] I have had some problems issues with that kind of people because, these bullies.  [Now the situation is clarified. For good writing, it is best to put them upfront.  You are writing an opinion, not a mystery novel.] Unfortunately, at there are many in highschools there are many like them and I cannot understand how someone can enjoy the pain of someone that those who had not done no anything wrong to them.

What also angers me is those people that who instead of doing something, they just stare gawk or even laugh when bullies do those their nastiness. things.

These people is not used do not to stop to think how the victim person who is suffering inside! that must feel.

Not bad at all. 

Something I cannot stand

I am an easy-going person who takes almost everything with a sense of humor. That is why I get on well with many people (you can also say: get along well with...), but there is a kind of people person that I really cannot stand.
The people who bothers and harasses weak people because they know they are not going to defend themselves make me sick. I have had some problems with that kind of people person (or those kinds of people) because, unfortunately, at highschools there are many like them and I cannot understand how someone can enjoy the pain of someone that who has not done anything wrong to them.
What also angers me is those people that instead of doing something, they (not really necessary to say 'they' again) just stare or even laugh when bullies do those things.
People is are not used to stopping to and thinking about how the person who is suffering from that must feel.

very good! There were just a few small problems that came from confusing person/people. Just remember:

person is

people are

Something I cannot stand

I am an easy-going person who takes almost everything with a sense of humor. That is why I get on well with many people, but there is a kind of people that I really cannot stand.
The people who bothers and harasses weak people because they know they are not going to defend themselves make me sick. I have had some problems with that kind of people because, unfortunately, at highschools there are many like them and I cannot understand how someone can enjoy the pain of someone that has not done anything wrong to them.
What also angers me is those people that instead of doing something, they just stare or even laugh when bullies do those things.
People is not used to stop to think how the person who is suffering that must feel.

'there is a kind of people' :  there is a (certain) type/kind/sort/ of person,   there are certain people

'people who bothers and harasses' :  people who bother and harass

'weak people' :  those they regard/think of/  as weak

'that kind of people' :  that kind of person

'those people that instead of . . ' :  those people that, instead of . .

'People is not used to stop to think' :  People do not stop to think (about)