To stir up trouble is to cause general discontentment, and some of our Kiwis might lovingly call a person who does this a shit-stirrer. Otherwise you have your mischief-maker, trouble-maker, or incendiary (normally meaning an arsonist). These all mean someone who agitates (or inflames:-) factions and/or promotes quarrels. That's pretty close. That is to say, an 'incendiary' doesn't necessaryily willfully promote unrest, as far as I know.
Many comparisons to animals are popular for the kind of people you're talking about - a snake in the grass, or a viper, serpent; these are pretty general, but nonetheless have an exact meaning when used in context.
I'm sure there is some term from Greek or Roman mythology if that's what you're looking for, I just don't know it. Only a harpy, Furies, or a Siren come to mind, none of which fit too well. That's the best I can do.
