I don't know if I was clear or not, but basically, I had two lines, and I used the interpolate effect between them. Now I want to cut some part of the result of interpolation out of my.. interpolation. But it doesn't seem to work. Did I do something wrong?

When you Interpolate the result is a group of objects. Ungroup them, and while having them all selected go to Path > Combine. Now you'll have one path with several subpaths and you can use rectangle to cut it. The rectangle will disappear after the cutting, select the cuts you wanted and group them together to preserve their arrangement.