Is there a WORD For: sound made by mouth to express demeaning annoyance or feigned, mocking disbelief?

Take your pick from this excellent article on annoying noises people make: annoying sounds

This one works well for what you are asking:

Alveolar, alveopalatal, or postalveolar click "Tongue-clucking." Specifically in disapproval. Often done with a slight upward detour of the eyes. Someone else has done something one simply doesn't do, darling, and we're not the sort of person who would actually voice disapproval — how base — but, you know, tsk. In short, an impatient, self-regarding, passive-aggressive condemnation. If you do this, try just… not… doing it.

1. Final rising tone: "Uptalk."

2. Final creaky phonation: "Vocal fry." The latest "OMG this new thing these kids do is going to destroy language!"

3. Fortis voiceless alveopalatal fricative: "Ssssshhhhhhh!"

4. Velar-ingressive linguadental fricative: "Sucking your teeth." Often this is to the side, not right in the middle.

5. Pulmonic-ingressive breathy-voiced rising-tone neutral vowel: "Gasp."

6. Fortis long final consonant with epenthetic neutral vowel: "Don't-tuh do this-suh." [My personal favorite]

7. Pulmonic ingressive voiceless alveolar glide and mid-central vowel, with optional unreleased final bilabial stop: Inhaled "Yeah" or "Yep."

8. Sustained mid-central vowel and/or bilabial nasal: "Uhhh… uhmmmm… mmmmm…"

9. Alveolar, alveopalatal, or postalveolar click: "Tongue-clucking." Specifically in disapproval. Often done with a slight upward detour of the eyes.

10. Loud long low back vowel with advanced tongue root and full oral opening: "Moose-call yawns."

The author, James Harbeck deserves a huge PRIZE for his priceless article!

There are 10 of them and so well described.

CLICK ON THE VIDEO in the LINK :)

I believe you're looking for the phrase "sucking your teeth." I didn't know what that term meant until I made that sound at a friend who said, "Don't suck your teeth at me!" Interesting article about it: http://www.telegraph.co.uk/news/worldnews/europe/france/11651574/French-schools-ban-teeth-sucking.html

Tsk tsk is the right answer. Although I guess there is another sound similar to it but it is made just once (and a bit as louder). One may call it just tsk. I don't know if in the literary community it has been universally accepted as a fact.

It involves separating both the lips also besides tongue and teeth. But quickly.

The combination of the quick separation - 1. of both lips 2. teeth and tongue from upper region of mouth (palate I guess) - make one sound that depicts frustration or disapproval.

I personally find it offensive when someone makes it even for genuine reasons. I wish no one did that.

Disclaimer. I do it sometimes myself. I try not do it.