I don't think you need to complain to your mum about him. You need to tell him.
Next time (if there is one) wait until he's said something that is clearly unpleasant, then interrupt and say "I really don't want to hear any more derogatory remarks from you" or "are you insulting me again? Please don't" or something else adult, assertive, unambiguous. Then stop. Dom't smile or giggle or look away. Don't get into conversation. If he flannels, say something on the lines of "No, you listen to me. I've had enough".
Avoid getting into a discussion about what he said, and whether it was really insulting or not. You can say you've told him, and you don't want it to happen aghsin. If he tries to argue, say the same thing, in the same words. Repeat as necessary.
If he does it again, yes, walk out. But make sure you've told him first. Keep it short.
Practice at home in private, or with a trusted friend. It can be difficult if you're not used to standing up to him. Getting into conversation or argument will enable your point to be lost a sea of how unreasonable and oversensitive youy are.
BTW, I reckon it is entirely normal for steps not to like each other. In some other species, step-dads kill or eat the existing young. Luckily we don't usually do that.