If it is a nice gash, I would avoid that area at least until the cut heals and the scab falls off. If it is a little, tiny nick, I wouldn't worry about it and I would shave right over it the next time.

Since I started, I have had one really nasty cut right below my eye. I just got careless and the razor sunk right into my cheek. I still have no idea how it happened, but it definitely left a scar.