Вы можете разобрать его самостоятельно.
const date = "20.05.2018, 10:21:37";
const [first, second] = date.split(',').map(item => item.trim());
const [day, month, year] = first.split('.');
const [hours, minutes, seconds] = second.split(':');
const newDate = new Date(year, month - 1, day, hours, minutes, seconds);
console.log(newDate);
Или с помощью регулярных выражений
const date = "20.05.2018, 10:21:37";
const m = /^(\d{2})\.(\d{2})\.(\d{4}), (\d{2}):(\d{2}):(\d{2})$/.exec(date);
const newDate = new Date(m[3], m[2] - 1, m[1], m[4], m[5], m[6]);
console.log(newDate);