While I've never cut into a mounting screw, my spoilboard shows considerable evidence of encounters with a too-deep Z cut.
On our multicam CNC there is a setting to limit and prevent any cut from going more than .001" (or your set amount) into the spoilboard. For every cut both the top of the work and the spoilboard top are set, so the machine "knows" where the spoilboard is and can keep programming/g-code mistakes from cutting into it. I'm getting into the habit of not trusting material to be consistently thick, and setting Z on the spoilboard rather than the material top. I don't set it at zero. I set it at a negative value of what I told Aspire the board thickness was. The guarantees that all through cuts make it through, and never do more than a skim cut into my spoilboard.
Mistakes can come from boring repetition, distractions when setting up a cut, or time-travelling parallel world generating events.
I'm glad to see you and the bit survived this one. A lesson learned, perhaps. 
On our multicam CNC there is a setting to limit and prevent any cut from going more than .001" (or your set amount) into the spoilboard. For every cut both the top of the work and the spoilboard top are set, so the machine "knows" where the spoilboard is and can keep programming/g-code mistakes from cutting into it. I'm getting into the habit of not trusting material to be consistently thick, and setting Z on the spoilboard rather than the material top. I don't set it at zero. I set it at a negative value of what I told Aspire the board thickness was. The guarantees that all through cuts make it through, and never do more than a skim cut into my spoilboard.
Mistakes can come from boring repetition, distractions when setting up a cut, or time-travelling parallel world generating events.