My daughter is hurting our cat

So I have the sweetest cat in the world who LOVES my daughter. I mean really, we ended up with this cat because she chose my daughter at just five months old and not because we wanted her lol my daughter has ALWAYS been really good about being nice to the cats. She knows how to pet gently and what not. But lately (as in withen this week) my 3 year old daughter has been wanting Penelope to play with her more and more and she doesn't understand that Penelope doesn't play like people do. When Penelope tries to walk away Jade runs after her and picks her up. Problem is when Penelope tries to get away at all she grabs the cat by what she can, wether that be a handful of fur, her tail, or an arm. Just today I looked over to see my daughter carrying her by her arm and throat! I of course did not let her get away with that but Jade doesn't seem to understand she was being hurtful. Penelope would never hurt Jade in a million years so there is never an reprocession for this behavior from the cat. Jade has no idea she's hurting that cat other than my to take my word for it. Which she doesn't of course. I'm afraid she's going to end up costing me an expensive vet bill if she doesn't stop. And even if she doesn't my poor cat doesn't deserve to be treated like this. I am at a loss for what to do. I don't want to spank because she is not purposefully being aggressive. And time outs arnt working. She is getting more and more obsessed with Penelope by the day and I don't know how to get her to understand.