What do I use to mount a heavy framed mirror to a stud wall?
You'll probably have an easier time using a picture hanger than a screw, and it will leave your wall in better shape when you remove it. Picture hangers transfer the downward force into pressure into the wall because the nail is mounted at an angle. The screw, on the other hand, is being bent because you're acting as a lever, where the stud is the fulcrum, the drywall is just empty space, and the wire is the force applied at the end. Even if you get a stronger screw, you're still placing a significant twisting force into the stud.

You can't use your typical picture hanger for a task like this. The small hangers that come in most kits are rated to only 20-30 lbs. However, you can find hangers like this one that is rated to 100 lbs (and I'd still use two of them, since it will make adjusting for level much easier and reduce the risk of failure).



The other option is called a french cleat which are two interlocking rails, one that attaches to the wall, and the other to what you're hanging. As long as you install them both straight and level, you don't need to adjust the mirror for level, and it distributes the weight across a larger area, reducing the risk of a failure.