I have SA and just started working as a beauty advisor in a store - which means my job is solely based on constant customer service. I have to say that I did not deal with my SA before getting started, so it was definitely an issue.
Not only do I have to deal with register/cash/returns/answering the phone/paging managers (which is terrifying cause I have to hear my voice echo in the entire store)/making sure I don't screw up when doing any procedures/etc, I have to constantly be looking out for costumers on my department and actively engage with them. Specially because I'm new both at costumer service and at the beauty department, I'm still learning everything. So that plus my SA leads to a lot of stuttering and forgetting how to do things and messing up my pages etc.
So I'm finding a few ways to not only make me more comfortable in my work place, but also when I mess up because of anxiety. 1) I need to make myself understand that I will mess up with some procedural thing - I am new, I don't know everything, and if I don't do it again, then it's ok. 2) If you stutter, make fun of yourself: "Hello, do you have your card rewards - I mean balance ca- Ah, ok let's start that again haha Do you have a balance rewards card? Oh I got it this time" and smile. People will understand and when you smile they get calmer and friendlier.
So yeah, basically understand you will make a fool out of yourself because of your SA - but please try and smile about it, making fun of yourself, so you can teach your body to understand that it shouldn't be in a panic mode because of that situation.