It means: "Don't annoy me." "Don't make me angry." It's something you'd say to someone who was bugging you, or teasing you, or otherwise getting on your nerves---warning them that you might lose your temper and respond in a way they won't like.
-Hey, Why are you drinking so much, dude?
-Don't mess with me.
by EverPino1D November 11, 2015
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