Edges can only be sharp if they are stamped in with sharp tools. You can clean them up the exact same way you stamp them in the first place, but you have to KEEP your tools absolutely sharp. Do no try to scrape them. Use a pointed scraper to scrape the background up against the carving.
Also, you don't necessarily need a vertical edge to your carving. I model leaves right down to the background and sometimes below. I think a lot of people are afraid to model. Apparently, I am not afraid enough, judging from the result; but if you don't over reach, you don't learn.