The Spectral Axe is crafted within an Infusement Altar. Spectral Axes are able to harvest a tree with 10 logs tall in one break.
On release, the Axe accidentally was able to be enchanted but was later fixed. But due to the bug, there could still be some enchanted spectral stuff out there.
Spectral Tools are not able to be enchanted or repaired. Repairing you will have to use another Spectral but repairing with other items like perfect diamonds is not possible.
In the development of the spectral tools, there was a thought to have the axe turn into a random axe between wood and diamond.