使用 Array#sort 方法和compare函数中的函数，通过获取差值来解析字符串并返回相应的值.

Use Array#sort method and within compare function parse the string and return value corresponding by getting the difference.

var arr = [{
  date: '2017-06-14 14:03:49'
}, {
  date: '2017-04-20 10:25:32'
}, {
  date: '2017-06-02 15:57:16'
}, {
  date: '2017-06-02 17:52:05'
}, {
  date: '2017-06-02 21:47:13'
}, {
  date: '2017-06-14 14:01:31'
}];

arr.sort(function(a, b) {
  // convert date object into number to resolve issue in typescript
  return  +new Date(a.date) - +new Date(b.date);
})

console.log(arr);

请参考git中的问题:对日期进行算术运算时出错

Refer the issue in git: Error when doing arithmetic operations on date

或参考: TypeScript按日期排序不起作用