My daughter has asperger's and ADHD, and often blurts out whatever she's thinking, no matter how rude/inappropriate it may be. I find it to be greatly embarassing, and I frequently need to apologize for her, but is there any way I can get through to her that certain things just aren't ok to say?

For example: "I can't believe your baby is so small when you were so big!" or "You smell bad"



ETA: She's 9 1/2, and extremely intelligent, but I have already tried reasoning with her and while she understands when I am explaining to her that saying things like that can be very hurtful, when the moment comes, she forgets and blurts out anyway.

Well, Freddy doesn't speak enough to say things like that. But he will hit and be rude in other ways physically. I tell him right away that it's not okay to do those things and depending on the situation, I have him apologize as well. Then I tell him some more appropriate behaviors. For example, instead of tackling a young child to the floor, I tell him to hug the child instead.
I'm sure it's more difficult since she's older. But I would have her apologize anyways, even if it wasn't intentional. Because it's hard for people with ASD to understand correct social behavior, I don't know if reasoning will work.
IDK if this helps. But keep trying!
My DH used to have problems interacting with people too. He used to hit kids with his lunchbox and hockey sticks and stuff and he had to learn from their reactions that it wasn't okay. No amount of telling him did anything. So I think you as a parent can only do so much.

My guy is just turning 5, so we haven't encountered that yet, I'm sorry I have no advice.
One of my oldest girlfriends works with autistic kids & teens, she is a life skills worker, and they work on that kind of thing. I'll ask her if she has any tips!

I did see these cards that are kind of neat for if your child has caused a scene, but maybe more than necessary for just an embarrassing comment... Autism Awareness Handout Cards (about halfway down the page)