That is the reason I originally was going to cut the ground cable.
Yeah, but this is where things go off the rails. That's not how you do something like this, even for experimentation. You don't lift the chassis from ground, you modify the rest of your apparatus' circuitry to work properly while still maintaining safety and sanity.
Before you even think about running something like this directly off the mains, you need to build your required style of circuitry in a low voltage version and thoroughly test everything. Then, once you have everything working properly in a low-voltage version, you can move on to making a
safe version of the motor power side and test it with your high voltage motor.
If everything were isolated properly with a transformer, you could theoretically modify the secondary, low voltage side with your control circuitry to run at the same potential as the motor side,
provided that everything to the control side was properly isolated with transformers and optocouplers with proper isolation and insulation. I'm not sure you understand the intricacies of doing that safely yet.
You could also just as easily design it with them them both isolated from each other (essentially as your computer PSU is originally, in stock form), again, using proper optocouplers and transformers, etc. so that it would always be properly isolated, regardless of what the potential at the actual motor is relative to your control circuitry. Then you still have danger in your motor area, potentially more dangerous than regular mains connected stuff since we're talking high current 400V, but can be done, provided you take all appropriate precautions. Again, I'm not sure you appreciate the danger involved with high energy, high voltage circuits in a configuration like this. This could easily be far more dangerous than the 120 volts that comes out of the wall.
One way or another, you need proper isolation! Removing the ground and running your control circuitry at 400 volts without isolation is not the way... That is lunacy. In some ways, that is even worse than the old hot-chassis TVs and radios.