Here are some tips for you.
When you've done your cuts, if they don't look smooth, then select the render with the magic wand, then go to Select > Modify > Smooth. Then smooth it by 1 or 2 pixels depending on the size of your render and you'll notice a difference.
Also if you've got parts of the background still visible on the render then go to Layer > Matting > Defringe. Then defringe it by 1 or 2 pixels depending on how neat your render is.
Hope this helps.