Dump this into Script Editor.app and run when you want to clear all notifications in the Notifications Center panel

clear-osx-notification-center.scpt.js

var app = Application("System Events");

var ncToggle = app.processes.byName('SystemUIServer').menuBars[0].menuBarItems.byName("Notification Center");
ncToggle.click(); // show Notification Center panel on screen right

var notificationCenter = app.processes.byName('NotificationCenter');
var ncWindow = notificationCenter.windows[0];
var ncNotifTabBtn = ncWindow.radioGroups[0].radioButtons.byName("Notifications");
var originalNotifTab = "notifications";
if(!ncNotifTabBtn.value()){
	ncNotifTabBtn.click(); // switch to "Notifications" tab if currently on "Today" tab
	originalNotifTab = "today";
}

var ncTable = ncWindow.scrollAreas[0].tables[0];
if(ncTable.rows().length > 1){ // ignore the "Do Not Disturb" hidden row
	var numNotificationGroups = ncTable.rows().map(function(row){
		return row.uiElements[0].buttons();
	}).reduce(function(allButtons, btnArray){
		return allButtons.concat(btnArray);
	}, []).filter(function(button){
		return button.description() == "clear";
	}).length;

	while(numNotificationGroups--){
		// doing this way instead of using Array.map above because the selector dynamically refreshes in the background instead of binding to the same object
		ncTable.rows[1].uiElements[0].buttons[0].click();
	}
}

if(originalNotifTab === "today"){
	ncWindow.radioGroups[0].radioButtons.byName("Today").click(); // restore to initial "Today" tab
}
ncToggle.click();