Script to sort alphabetically the completed reminders in Apple Reminders. Written in JavaScript (works in Yosemite).

reminders-sort.js

var listName = '<list name>'

var Reminders = Application('Reminders');
var list = Reminders.lists.byName(listName);

var done = [];
var reminders = list.reminders.whose({completed: true});
var rl = reminders.length;

Progress.totalUnitCount = 2 * rl;

for (var i = 0; i < reminders.length; ++i) {
	var n = reminders[i].name();
	
	if (done.indexOf(n) >= 0) {
		reminders[i].delete();
	} else {
		done.push(n);
	}
	
	Progress.completedUnitCount = i;
}
	
done.sort().reverse();

for (var i = 0; i < done.length; ++i) {
	list.reminders.byName(done[i]).completionDate = new Date(1000 * i);

	Progress.completedUnitCount = rl+i;	
}