DropRedFred I don't know if you're going to see this a month later but I really wanted to add my 'two cents', so to speak. I see its been said in so many words before but I cannot emphasise enough how very hurtful and damaging, both to your daughter, her relationship with you and future men in her life, this sort of behaviour is if allowed to continue.
It is her cat, her responsibility and her new step father is mocking it. Whilst it can be argued that it is 'only a cat' and she is being too sensitive, in context she is reacting to a grown man, a new person who is now competing for your attention at a very sensitive stage in her life, directing negativity towards her.
It is a very confusing issue as there is a fine line between 'family banter' as one poster suggested and subtle bullying and put downs. The point is the motivation behind it. The fact that your DD has made derogatory comments about DSS's hamster has most likely annoyed DP however instead of dealing with it in an adult manner has 'taken sides' with his son, attacking the cat.
I thought very carefully before answering this question but I have observed this sort of thing all too often and I don't think people take it seriously enough or quite understand what is going on.
So to answer your question, no YANBU and it needs to stop.