To engage in an aggressive attack against someone without holding back or showing any mercy; to attack the most vulnerable part of someone. The phrase is usually (though not always) understood as referring to a non-physical attack. Similar to the phrase "go for the jugular." This is politics, and the candidates aren't going to play nice during the debate—they're going to go for the throat any chance they get. If you tangle with him, don't expect a fair fight—he'll go for the throat.