It really depends on how bad the cut is, the overall health of the clown, and how good the water parameters are (( to limit stress induced secondary infections ))
To make you feel better, about a month ago my male Clarkii tried to boss my purple tang around. He ended up with a nice cut for his troubles (( was deep enough that it the white of his stripe was gone, and it was red )). Two days later it was all healed up and couldn't even see a make. I actually was watching the tank when he got cut.