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1.
To "suck your teeth" at someone is literally the process of sucking your teeth. A sound can be made by clenching your teeth together and then making a sharp sucking motion as if inhaling inhaling ice cream through a straw. The harder you suck the louder the sound. It is usually done out of annoyance at another person.
"Don't suck your teeth at me!" said the angry teacher the the student.

Jeremy rolled his eyes and sucked his teeth at Jerome's bad joke.
by Dutch84 March 20, 2005
 
2.
A great way to get me not to do your yuppie ass a favor.
" Don't suck teeth at me it's not my fault! I said I don't care..."
vs.
"I guess the easiest way to say this for you is fuck off!"
by ayobeslim November 16, 2013
 
3.
also called "stiups" or "stiupsin" in tha caribbean and west indies. (jamaica, tt, etc.)
TRINI: she get vex bcuz i stiupzz @ she naggin

ENUNCIATIN ANNOYIN KNOW-IT-ALL AMERICAN DUDE: i do so believe you mean "She GOT angry because I SUCKED MY TEETH at HER"

TRINI: shut up. itzz stiups, not no suck teeth
by SICKofMLIS December 29, 2005
 
4.
To "Suck Teeth" means to make a sound via your mouth, inhaling sharply and using your tongue.

Many have argued what the spelling of this sound might be, but after careful consideration of all feedback, <Element|Rasta> came up with the defining spelling. This is:

chmishsyeursishchrish
Suck Teeth

<element|Rasta> me- eh bwoy gway so from here for mi bruk up ya raas seen
<element|Rasta> boy- fcuk of old rasta you a old grumpy bastard
<element|Rasta> me - chmishsyeursishchrish, dont make me lick ya up wi su-in bwoy, ya like bangalu to bomboclaat bwoy
by RastaMan May 25, 2007