Crazy ManMan started following Noise, Hemophobiacs Getting Scared of Blood Stains on The Walls etc., Kate and and 2 others
So about the cutting off limbs in the walking dead:
The whole apocalypse started by an infection so when you die and when you get bitten the infection goes to you and spreads up to your brain. ( If you have watched the episode "TS-19" then you have been explained this already) they immendietly cut off the limb to stop the infection spreading. I understand that loss of blood is a big death situation but this is the only way to stop the infection spreading . They put pressure on the amputated limb and patch it up with a lot of bandages which obviously stops the blood a little. I think it's a little risky but In most occasions where they do this the victim/ patient is an important aspect of the group like
Hershel: he is a doctor.