How to overwrite Ctrl-x to not cut lines?

Ctrl-x cuts the current line when nothing is selected. That's great. BUT, as an emacs user, I have the habit to hit Ctrl-x-s to save a file. With any other editor it is fine because if nothing is selected, Ctrl-x has no effect. BUT with Sublime Text, it cuts the line... and saves the file! This is destructive.

How to overwrite Ctrl-x to not cut lines? and just cut selections?