Miru Eyes can be obtained from Mirus either by killing them or taming them and harvesting from them when they are your Pets, and from or Corrupted Mirus as a drop in their Loot Bags.
Arctic Mirus on the other hand have blue Arctic Miru Eyes that cannot be used in the same recipes, just as ordinary fiery red Miru eyes cannot be used in recipes that demand Arctic Miru eyes.
Dark green ordinary Mirus with golden eyes live in caves and underground on the Stalactite layer. They mainly spawn on Siltstone or Stalactites in the darkness. They can ascend from this layer easily and so can even come out of caves to the surface at night. But if sunlight hits Mirus, they will burst into blue flames and perish.
Violet Corrupted Mirus live in the Corruption layer deep underground and will spawn on any corrupted material or block that has not been crafted. They will only spawn in darkness as well, but can prevail in sunlight.
You can obtain reddish-golden Miru Eyes from Corrupted Mirus only when killing or dismissing them and will receive them as a drop in their Loot Bags, however (currently as of March 2016) you can not obtain these eyes when harvesting from Corrupted Mirus if they are your Pets.
All kind of Mirus are aggressive creatures that will pursue and attack player-characters when they get close enough, except on worlds set to "peaceful".
Miru Eyes are needed to craft Obsidian Swords and Obsidian armor in the crafting menu (opened with "q" as the default key).