It has the largest base damage of any axe in the game (with the exception of the Fire Axe and End Times Axe on Lava Wood and Phantom Wood, respectively), but also has the slowest swing cool-down of any axe in the game, severely hindering its usefulness. The description, when it could be 'checked' in Bob's Shack during the event, very likely refers to how mosquitoes or other insects used to get stuck and fossilized in amber in the prehistoric ages in real life, however, no instances of mosquitoes have ever been reported, and it may only be a tease. The head of the axe is also visibly transparent, and when held up to an item, players have the ability to see through the axe-head, though the image seen through it may be slightly distorted.
There once was a glitch where an unboxed Amber Axe would have no texture on the handle. After it was dropped, the Amber Axe entirely turned into Amber and could no longer be put into the player's inventory, but could still be moved around. This would happen when the Amber Axe was on the ground when the player reloaded their property. (this glitch has now been fixed) (There was also a known bug where the texture from the axe would appear on the grass, making the grass look like swamp water.) This feature has since been removed.