It wouldn't be a Genre, But if you're talking about the type of mash-ups that Super Smash Bros do, then its most commonly called, "Dubbing" or "Dubs." It's an art of Turntablism, that's actually pretty competitive between people who take it seriously. I forget what the record is for most vinyls played in one hour in such a style, but it's over 100 IIRC.
Link me to an example, I'm not sure exactly what you might be talking about though. There's Dubs, There's Remixes, Remakes, etc.