This type of kidney surgery is most often done as a first step in certain kidney cancers and when it is important to maintain kidney function. Percutaneous nephrolithotomy/nephrolithotripsy (tunnel surgery): Percutaneous nephrolithotomy and nephrolithotripsy are both used to remove kidney stones.onditions treated by kidney surgery include: 1  kidney cancer; 2  chronic kidney diseases; 3  kidney stones (removal); 4  kidney infection; 5  renal hypertension; 6  traumatic kidney injury; 7  kidney donation.