The man cut his right hand in the fight with the police.
And he had to cut his hand to do it.
He had cut his hand on a piece of glass.
"How do you know he had already cut his father's hand?"
"She cut her hand on a knife and lost a great deal of blood."
I would rather cut my hands off and blind myself in one eye.
Somehow, he had cut his hand and been forced to leave the game.
He had indeed badly cut his hand going through the glass.
Have you ever cut your hand on the weekend and gone to an emergency room?
You're not at all well, and you've cut your hand.