You can traverse through the array and find the index and then do a splice.
var array1 = [["Ben", 17, 1], ["Susie", 12, 0], ["Thomas", 21, 1]];
console.log(array1);
for(var x=0; x<array1.length; x++) {
if(array1[x][0] == "Susie")
array1.splice(x,1);
}
console.log(array1);
here is a fiddle.