[DownTownTonyBrown]

Off his mitt and then caught...? That's a foul tip (because it hit the mitt first) and a catch. Runner can advance and batter is out.

Check your case book 2.16.1 COMMENT (4)
A pitch touches the bat of B2 in (a), it goes directly to F2's glove, then into his protector and rebounds into his hand or glove or (b)it goes directly to F2's protector or mask and rebounds into his hand or glove. In (a), it is a foul tip and a catch. In (b), the ball becomes dead when it touches the body of F2 and is an uncaught foul. In a related situation, a foul ball rises (emphasis mine) and comes down to strike the catcher's mask or protector and then rebounds into his hand. It is a caught foul. B2 is out and the ball remains alive. (5-1-1d. 7-2-1d)

Checking the definition of a foul tip... 2-16-2
... a batted ball that goes directly to the catcher's hands and is legally caught by any fielder.

Who has seen this happen? bounces off the catcher's mitt and F3 catches it on the fly - 3rd strike on the batter and ball is live.