When replacing a ball joint on a Chevy Cavalier do you have to remove the control arm?

No you don't. But you might want to replace the lower bushing also since you will be half way their. Also it is easier because you have to grind off the rivets to get the ball joint off the control arm. Most garages replace the control arm because labor rates compared to the cost of a new control is less expensive for the garage and customer. Also the liablity of the new ball joint has to be bolted on and not riveted as factory unit.