Some of the catching experts may offer better advice, but I would offer a few suggestions.
First, make sure you're catching the ball in the proper place in the mitt. Some catchers try to catch the ball out in the pocket, which can lead to an inability to control the mitt when receiving a pitch. The ball should be caught at the point where the palm meets the pocket, basically between the thumb and pointer finger. I have seen this help a lot of catchers control the mitt, both on pitches down, and pitches away from their body in general (inside or outside).
Second, after you give your target and the pitcher goes into their windup, don't keep a rigid target. You should relax your mitt and receiving arm before receving the pitch. Some guys simply let their wrist go limp and pull their mitt towards their body a few inches. Some guys will turn their glove approximately a quarter turn towards their left (assuming a right hand thrower) and pull the glove back towards their body slightly.
Then when the pitch approaches they go out and "beat the ball to the spot". If you keep a rigid target, this will almost force you to "stab" at low pitches. The combination of you stabbing plus the force of the pitch will jerk the mitt downward a few extra inches. Instead, after relaxing your mitt, go down and get below the pitch and catch the pitch with your mitt going forward and upward slightly to offset the downward force of the ball. Then don't pull the pitch up any further.....try to stick it right where you catch it.
If it's a ball, don't try to pull it up into the strike zone. Just try to stick those borderline strikes. Remember, you're not trying to steal strikes...you're just trying to be sure that strikes look like strikes, and maybe occasionally you'll get a borderline pitch.
And of course, strength in the hands and forearms won't hurt you. I'm not sure I was overly clear, but I hope this helps. I'm sure some of the other catching guys can offer much more eloquent advice.