The Living Axe is a tool added by Roots. Unlike regular axes, it will heal over time; each tick, it will have a 1/80 chance to restore one durability (so there is about a 22.25% chance of at least one durability point being restored every second).
Your rituals are capable of channeling life energy into previously dead objects. Using this, you can grow newer, stronger forms for your wooden tools. Adding a little gold for reinforcement, as well as a verdant sprig to grow upon, will grant you tools of similar strength to iron that repair slowly over time.