I loosen the tension first, then cut them. In my guitars, they usually started breaking about an hour after I thought they sounded dead...I got really good at changing guitars mid-song though; my bandmates were always a little awed by that(the only part of my playing they were awed by...)
I would remove schmootze from a Strad, it ain't part of the sound...some people goop up their fretboards and I guess that becomes part of their sound, but maybe they should wash their hands more...