The answer is in the title. 
A negative person will go after others trying to spread the negative energy they are carrying. But there is a reason for this.
They don’t want to carry this negativity alone. By getting someone else upset, they get to unload some of that negative energy onto the other person.
Silence works best here. Even if you try to laugh them off, they can still sense they’ve affected you in some way. But with silence and indifference, they have nothing to work with.
How do you handle a negative person?

A negative person will go after others trying to spread the negative energy they are carrying. But there is a reason for this.
They don’t want to carry this negativity alone. By getting someone else upset, they get to unload some of that negative energy onto the other person.
Silence works best here. Even if you try to laugh them off, they can still sense they’ve affected you in some way. But with silence and indifference, they have nothing to work with.
How do you handle a negative person?