We need to know a little bit more information. By you saying it "cuts off", are you meaning the fan? As in, NO air comes out of the vents, regardless of temp? Or are you saying that you floor it, the fan stays the same, but the air goes warm?
Typically, if you FLOOR any car of late, the computer in the car knows that "Hey, I need all the power I can get, lemme disconnect the AC compressor". To put it in lamens terms (BTW, I LOVE my spelling).
Give us a few more clues, we might be able to help.
James