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To "Sip Your Tea" means that you are basically just going to mind your business since whatever situation is going on most likely does not concern you.
Ex:

girl one: "Ooooh girl did you hear how Josh cheated on Tiffany!?"

girl two: "Omg well I'm just gonna sip my tea like its none if my business."
by thatsfugazi December 09, 2014
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