I despise my mentally handicap sister
Why do you say that you despise her?
She is always causing tension in my home, without her it would be much more peaceful
I do not think that she does this on purpose. You should try to just move past this and try to be more understanding and accepting.
I'm going to find the perfect time to get rid of her.
Sibling issues are not uncommon, but you can't simply get rid of her. You should make an effort to be more patient with her and perhaps help her in situations so tensions in your family can be reduced.