I'm going to kick my grandma out of my house
For what reason would you kick your grandmother out of your house?
She's always so ungrateful of everything I do for her
I feel like we've all experienced an ungrateful family member at one point, but your grandmother is elderly and kicking her out could have very serious negative ramifications for her. Instead of doing something so extreme, try talking to her about her actions and how they make you feel.
I could take care of her but I don't like to live with ungrateful people.
I totally get that you don't like how your living situation is making you feel. The reality though is that she depends on you to take care of her and as such, it's important you talk to her seriously, but calmly. She shouldn't be kicked out, but you shouldn't be uncomfortable in your own home.