Removing Contaminated Gloves

When you’re double gloved, how do you remove both gloves in the middle of a case if they become contaminated?

During a case, I accidentally poked my hand with a clean, unused suture and it definitely punctured both gloves. I discarded to suture of course. But want to make sure I did the right thing when I had the circulator remove both of my gloves. Can someone explain what to do?