Basically you're requesting to play...without music... ? (I dunno what "background music" could be...) If it is so, do as baraatje said and you'll be fine
I mean, when osu! is in background (Alt + Tab) audio will stile continue playing. If you want to listen something else on the way (maybe the demos of the downloable beatmaps on the website) without osu! audio you have to pause it everytime.