Meaning
'Nuh draw mi tongue' — don't draw my tongue, that is, don't provoke me into speaking, or you'll get an earful of hard truths. It is a warning to someone who is pressing or needling you: keep pushing, and you will make me say the blunt, cutting things I have been holding back out of restraint. To 'draw' a person's tongue is to goad them into the plain, wounding speech they were biting down, and the phrase is a last caution before the gloves come off and the unsparing words come out.
Examples
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Nuh draw mi tongue, cause mi will tell yuh di whole truth.
Don't provoke me, because I'll tell you the whole hard truth.
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Him keep pushing till mi cuss him off — nuh draw mi tongue!
He kept pushing until I cursed him out — don't get me started!
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Mi a stay quiet, so nuh draw mi tongue.
I'm staying quiet, so don't provoke me into speaking.
Origin
'Draw' here means to pull or provoke out; to 'draw' someone's tongue is to goad them until they let loose the sharp words they were withholding.
How it’s used
A warning to someone provoking you that they are about to make you say things they won't like.