[Stiglr]

In the dialog where you set the A and B operands of the Boolean, check the little box that says something like, "Keep original" or something like that. Check it for both the operands and I believe the result should be just the cut piece remains.

I say should because I've had some problems getting the results I have wanted with Booleans... but, what you want IS possible in some way. Monkey around with the settings and you'll stumble on it.