What is the technology of slicing a chip to debug called?
It is unclear what technology you mean as there are many. Go here to see a list. 

Find more by searching for "Semiconductor Failure Analysis".

"Slicing a chip" is destructive and not so much for debugging as for reverse engineering.

When designers know what the bug is and want to make circuit changes and/or experiment to confirm their findings, usually non-destrictive methods are used like Focussed Ion Beam (FIB) to make small changes to the circuits on a chip.