I've had the same question, wanting to delete a slot/slots out of a 5 slot performance right from the Profiler.
My solution has been to delete in Rig Manager, or if not connected to Rig Manager, uncheck the Slot Enable box.
The beauty of the Slot Enable uncheck is, if you decide you want that rig back, you just check the Slot Enable box.
And of course, you can overwrite the slot at anytime.
Alternatively, you can copy and past the slots you do want to keep to a new performance, and then delete the old performance. (I just checked, and I can't find a way to delete a performance at the profiler, so you may have to do that from Rig Manager also. )
If, as paults asked above, you want less than 5 slots in a performance, you can change that in the Systems settings, it's on page 12 of 18.
Whew, whoever said life is just a bunch of workarounds was RIGHT!