Apple - Can a keyboard shortcut force TextEdit windows to close and discard all changes?

tell application "TextEdit" to close (windows where name of its document is "Untitled") saving no would close all untitled documents without saving them.

You could close the current window with tell application (path to frontmost application as text) to close window 1 saving no. It would close all tabs in some applications that use tabs though.

It's easier to just press ⌘W⌫ in my opinion. You can disable the animation for showing the sheets with defaults write -g NSWindowResizeTime -float 0.001.

If you hit cmd+option+q to quit the app (or hold down Option while quitting from the main menu), it will give you the option to discard changes in all unsaved windows at once, rather than having to tell it to discard changes in each window individually. This will work with all Apple apps, not just TextEdit.