[Inkscape-user] Cropping an object?

I'm trying to make a little logo/startup screen/wallpaper. I've attached an example which should make it clear what I'm trying to do. I need to make the swirl disappear behind Tux. What I'm thinking (coming from raster editing) is to crop the swirl at the points where it and Tux meet. I can't find a way to do this. I've tried editing the nodes, but moving one node changes the whole shape of the swirl.

Is there any way to divide an object into two parts with a line? Is there a way to do what I'm thinking? Any ideas at all?

Thanks.