你的意思是arr1[0][0]===arr2[0][0],就取出arr2[0]里面除了arr2[0][0]的值？

随便写了个，还没考虑的情况有很多。
function getRestArr(arr1, arr2) {
    var result = [];
    arr1.forEach(function(item, i) {
        var len = arr1[i].length;
        if (JSON.stringify(arr1[i]) === JSON.stringify(arr2[i].slice(0, len))) {
            result.push(arr2[i].slice(len))
        }
    });
    return result
}
var arr1 = [
    [1, 2],
    [3, 4]
];
var arr2 = [
    [1, 2, 8, 74, 2, 3],
    [3, 4, 56, 8, 14, 9]
];
console.log(getRestArr(arr1, arr2))

var arr1=[[1,2],[3,4]];
var arr2=[[1,2,8,74,2,3],[3,4,56,8,14,9]];

for(var i = 0; i < arr1.length; i++){
    for(j = 0; j < arr2.length; j++){
        var arr1_str = arr1[i].toString();
        var arr2_str = arr2[j].toString();
        var arr_str = '';
        var _index = arr2_str.indexOf(arr1_str);

        if(_index != -1){
            arr_str = arr2_str.substr(_index+arr1[i].length+2);
            console.log('========================')
            console.log('arr1_str',arr1_str)
            console.log('arr2_str',arr2_str)
            console.log('arr_str',arr_str)
            console.log('_index',_index)
            console.log(arr_str.split(','))
        }
        
    }
}