Вот решение с правильно отформатированным массивом.
let arr = [
{ name: "Angel", data: "random data", New_date: "2020-12-10" },
{ name: "Tom", data: "random data", New_date: "2019-11-10" },
{ name: "Tom", data: "random data", New_date: "2020-11-10" },
{ name: "Angel", data: "random data", New_date: "2020-09-10" },
]
console.log('ascending', arr.sort((a, b) => new Date(a.New_date) - new Date(b.New_date)))
console.log('descending', arr.sort((a, b) => new Date(b.New_date) - new Date(a.New_date)))