If the cut is clean, i.e. amputated by a scientist or vet there are no drawbacks to the regenerated limbs, but if they get into fights with other axolotls and the limbs are "half-off" they sometimes regrow deformed.
They have a nervous system and DO feel pain, afaik the extent of pain they feel is not really known.
A vet had to amputate a limb of an Axolotl I keep as a pet because he got into a fight with another one and he did not even finch.