Is this considered child abuse or is it just discipline?

about a an hour ago, my little sister was jumping on the bed and my grandpa told her to stop, so she did. then she went to go pet our dog( cane corso) and she was on top of our dog and my grandpa told her to get off of her, but she wouldn't listen, so he went over to her, and she said kept saying no in a frightened voice and he jerked her up by her left arm and smacked her on her butt and she started to cry and he told her to "shut the f*ck up." then he let go of her and went back to sit down and he said to me and my older sister " she is nothing but a f*cking brat. one of these days Ezzy( our cane corso) will bite her head off" and my little sister told him to shut up and he said " go f*ck yourself you don't tell me to shut up. little f*cking b*tch." and then he was like to me and my older sister "when she grows up, no one will want to play with her, she won't have any friends." and my little sister said "no" and he was like "shut up you little brat." and after that she went to pet our chihuahua, and my grandpa was like "you leave her alone. don't touch her." and my little sister didn't listen and she kept on petting our chihuahua and my grandpa went over and smacked her hand really hard and she started to cry again. and he was like " you don't touch her." and then he was like to me and my older sister, " one of these days, bambi(our chihuahua) will bite her and break the skin and then Bambi will get in trouble and have to get put down." and then my grandpa goes and tells my mom that my little sister was poking our dog, but she was really petting her.

i feel really bad for my little sister, but i don't know if i should tell my mom, because she will only say "she deserved it, she is nothing but a little brat." what should i do?