As mentioned, whatever gozinta the hole presumably needs to be connected, and that leads to a question about "why under power?"...
You oughtta turn off power. Obviously.
Now, just as a point of discussion, if I HAD TO do this with the power ON (and I mean HAD TO), here's what I would do.
1) open the door (in many cabs that turns off the power, but never mind that)
2) Cover the open cab with a sheet of thickish plastic. Not bag material, I mean fiberglass, lexan, etc. Preferably something opaque with 94 V0 flammability
3) Securely prop the open door in position, and do the work. Your choice how to cut, sabre saw or whatever.
4) reverse the process to close it up.
Yes, basically same as what Extropic said.
I am not recommending this. But if you really had to do it, that would be a possible way with acceptably low risk for a "have to" situation.
As to how the "whateveritis" gets connected, your problem, dunno where it goes etc. Presumably it connects to something already on the door, at low voltage/current, or to something that can be shut off to do the job.