Suck is short for "your dick sucker" meaning mouth.
Shut your suck is a derogatory way of telling someone to shut up. Used a lot in the military and law enforcement communities with people who are deemed lower in social ranking (such as lower enlisted military or perps for law enforcement).
" Shut your suck" short for shut your dick sucker when someone just won't shut up.
by Elle Blank June 29, 2008

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