Looking at the specifications on that mixer, it has a DC motor
inside and not an AC like most of the others.
So, there is a board and driver inside the mixer to change the power over for the motor
It appears something in the circuitry is creating enough leakage that the GFCI thinks there is a major problem and shuts down.
I have a kitchen aid myself but just not that big, and it is an AC motor
and have no problems.
I would do the test I suggested earlier and try a different circuit just to be 100% sure nothing is wrong on the electrical inside the mixer.
if it runs fine on another circuit NOT ON a GFCI, then something inside the that mixer changing the power over is creating a false sense to the GFCI.
If it quits on a standard receptacle circuit, there is something wrong and needs to be exchanged.
I do not know any way around operating it in the kitchen since they are all GFCI for protection.
Counter top receptacles are supposed to be GFCI protected.
I do not know if the manufacturer has had any other complaints on the same issue or not. But will try to search to find out.