A) You'd bleed out when this thing severed every major bleed vessel in your arm/leg. Muscle tissue also tends to have a good blood supple, so it bleeds a lot too. Most amputations are for limbs with poor circulation, but the amputation site has to be high enough to have good blood flow or it'll never heal.

B) You want to leave a flap of skin so you have something to cover the stump with. Ditto for not leaving half severed muscles & such.

In the days before anesthesia surgeons prided themselves based on how fast they could operate. When somebody is sawing off your infected leg you'd much rather have only 2.5 minutes of agony with "Time me, gentlemen" Liston instead of 10 - 15 with a more slow & methodical surgeon. Even then they didn't just chop it off with a guillotine, there's a bit more finesse to the process than that. If you want the patient to survive at least... which they had a 50-50 shot of.