I cut close to the edge of one piece, then pin it on the wider seam of the next so it won't slip when I sew them together.
I use wet paper towel to make the edge as smooth as possible for a good connection.
I always trim as much off the edges and then butt them up together before doing the zig zag stitch. Then give a little rinse. You will want some left in to keep the shape firm for the box. That is a pretty design.