standard program for cutting music: Audacity (its free)
BUT
starting off mixing, you can use something called Virtual DJ - its terrible but allows you to get the basic jist
i currently use Mixmeister fusion for mixing. you just have to fiddle EQ until you (sort of) seperate certain things. although it will sound choppy. also, hit up youtube.
type in the track name, then "instrumental" - occasionally some sexy individual has posted up the seperate layers of the track.
to be honest, i use my music software for remixes, as opposed to mixing software. hope that helps