The Arm-Mimics identical to the Mask-Mimic aside from not having a mask. They move by mirroring Link in opposite directions. If you move up, they will move down. If you move left, they will move right. A sword slash will do nothing but push the Arm-Mimic back. To kill them use spin attacks or charge through them with the Sword and Pegasus Boots. It resembles a potato-person.
In Link's Awakening Arm-Mimics are found exclusively within Dream Shrine, Turtle Rock and the cave where Link obtains the Magnifying Lens. Arm-Mimic's found in this cave are invisible and can only be seen with the Magnifying Lens. It is easiest to defeate them by using a Spin Attack or Charge Attack makes it easier to defeat these enemies. Arm-Mimics deal three hearts of damage, making them the strongest enemies in the game.
Oracle of Ages and Oracle of Seasons
The Arm-Mimics in Oracle of Ages and Oracle of Seasons look and act exactly the same as in Link's Awakening. The differences are, they can withstand more damage, they cause only one heart damage, and they can be defeated with and normal sword slash. They are found in various dungeons.
To get defeat them, either back them into a wall, or move carefully so that they will slowly move towards you, and slash away at them a few times with your sword.
Orange Arm-Mimic Sprite from Link's Awakening