A control valve apparatus adapted to be positioned within a subsea blowout preventer stack for controlling the flow of fluid from an offshore well includes a ball valve element provided with the capability of cutting coil tubing typically employed in well workover and completion operations. The ball element has a cutting edge that coacts with the valve seat to shear the tubing, and a relief slot that receives the tubing during cutting to prevent the tubing from being placed in double shear. Hydraulically operable means is provided to assist in closure of the ball valve element and consequent cutting of tubing extending into the well, in case of emergency.