I always cut things out section by section. For a few reasons, 1) the one above 2) If you accidentally double click or click to close to a last point and then it selects all your work that you didn't want it can get frustrating 3) It's just safer and you can be more precise!
If you zoom in about 400% and use your tool section by section, you will get a very decent clean cut and can go into much more detail with hair and all those other things that arent curves or straight lines.
Like my current Sam Fisher signature. His hair (cant really see it when shrunken to sig size) but anyways it looked really good once I was done and I zoomed in I think at 600% ... Anyways i'll stop rambling now