You use the cuff from the sweater you are cutting up for the cuff of the mitten.
I had this gorgeous felted wool sweater to small to wear in my closet for years just waiting for the right project. It didn't have sleeve cuffs so I improvised and used the top part of a sock.
There is a link below the you tube video made by roman cake designs that takes you to her blog where there is a free downloadable pattern. The pattern is for a small to medium.
I suggest before you use your nice sweaters to make one with something you don't care if you have to throw it out due to "the learning experience" my first one was way to small so I added a half inch all the way around the patterns and then made this pair out of denim.
Making this denim pair I realize that you really need the softness and cushiness of a sweater. See what happens by the thumb part? This may have been my mistake in sewing but using a sweater you probablly wouldn't even notice.
If you live in a cold climate you really should try this.
I know you have a favorite sweater in your closet you can't or don't wear anymore.