No, in DF axolotls do not regenerate any limbs or organs they lose as it is right now.
As for modding such a thing in, the best you can do right now is make them briefly transform into another creature for a split second or so to insta-regenerate any lost limbs or other such missing body parts. To do Something like that first make a text file like this:
interaction_aaa
[OBJECT:INTERACTION]
[INTERACTION:REGENERATE]
[I_SOURCE:CREATURE_ACTION]
[I_TARGET:A:CREATURE]
[IT_LOCATION:CONTEXT_CREATURE]
[IT_MANUAL_INPUT:creature]
[I_EFFECT:ADD_SYNDROME]
[IE_TARGET:A]
[IE_IMMEDIATE]
[SYNDROME]
[SYN_NAME:regenerate]
[SYN_CLASS:REGENERATE]
[CE_BODY_TRANSFORMATION:START:0:END:1]
[CE:CREATURE:BBB:CASTEHEAL]
Wherein AAA is to be replaced with the creature that is to be healed and BBB is the creature that AAA is to be briefly transformed into.
Then put something like this in the creature's raws:
[CAN_DO_INTERACTION:REGENERATE]
[CDI:ADV_NAME:Regenerate]
[CDI:TARGET:A:SELF_ONLY]
[CDI:WAIT_PERIOD:TTTT]
Wherein the TTTT is the amount of waiting time before the creature can do the interaction again. If this is not suitably long enough, the creature will spend all or most of its transforming. The time is measured in
ticks. Note that this is the only way
I know how to do this. There might be a better way to do this, but if there is I am unaware of it.
Also note that this will only fix all non-fatal wounds, and the brain can never be regenerated as even so much as a bruise to that organ is fatal as it is in DF right now.