A-series

Don't cut the frame, it's not necessary.

The only torque mount that the car needs is the rear mount. If you're using stock rubber mounts it's best to have the front mount(s) helping but for normal daily driving it will be fine.

I'd try drilling out what remains in the threads (spray liberally with PB Blaster before you try, both from the bottom and top by sticking the straw into the pre-existing drain holes in the frame) but if worse comes to worse you can drive the car without the lower left torque mount.

I'm a little confused though, is the bracket already off the car? If the bracket is still on the car, you can remove the A/C belt by only removing the center rubber insert (and leaving the bracket in place) or even without removing the center insert but it would be more difficult/a tighter fit.

The 4 thin rubber connections that hold the rubber insert in the left front bracket aren't important and will either already be broken/missing or they can be cut, just make sure when you reinstall the center insert that the orientation is correct after the nut is torqued down. Holding it in place with one hand while you tighten it down a bit helps.

If you have already taken the braket off the car by this point (and are unable to reinstall it) I would leave the center insert on the lower left A/C 'rod' (cutting the 4 thin rubber connections to the bracket if necessary) because it will still help during acceleration. The brackets for the lower front torque mounts are there to give added support during engine braking but as long as the rear mount is there and secure, those brackets are a nice extra but aren't needed if worse comes to worse. The engine will torque/rotate far more under acceleration than it ever could from engine braking so I doubt the other mounts would even notice that the front left bracket is no longer there.