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."
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 9, 2014