This is supposed to be pretty controlled and minimally invasive (so to speak) surgery. The probability of amputation is pretty much nil unless you have a blood clotting disorder, collagen/vascular disorder, atrial fibrillation, or something else really bizarre.
Amputation occurs when the arterial blood supply to the limb becomes compromised. That can happen during trauma easily because so much gets damaged. That's where most amputations in young people come from. It can theoretically happen if you develop a septic infection post operatively (as it happens for people with meningitis), but this is unlikely of course. It can theoretically happen as well if your surgeon is an absolute butcher and maybe "slips" during cutting the bone, slicing through major tissues/vessels, but this also of course is highly improbable, since they're only making small controlled cuts.
Doctors quote the risk because anything can happen and they don't want to be sued into oblivion if it does. It doesn't mean it's likely or realistic to happen.
If anyone ever lost a limb during routine cosmetic limb lengthening, I'd be curious to know how. You're probably more likely to die from an adverse anesthetic reaction or fat embolism than you are to lose a limb.