Once there lived a wicked asura by the name Gajamukh. He was the king of asuras (demons). He wanted to rule over gods and humans too. He decided to please Siva to get his wishes granted. He started severe penitence for years. At last Siva was pleased and appeared before him. He asked for many powers. The most important and dangerous one was that he could never be harmed by any weapon. Siva granted him all his wishes.
Gajamukh became very arrogant and started misusing his blessings. He started attacking everyone including sages, humans and all living creatures. He even started troubling gods by attacking them. Gajamukh gave an order instructing everyone to worship him. Infuriated by his arrogance, Siva asked his son Ganesha to punish the asura. A severe battle between Ganesha and the asura ensued. Ganesha could not defeat him for a long time because of the boon granted to him. Finally he broke his tusk and threw the piece on Gajamukh. He was wounded badly, but was not ready to accept defeat. He took the form of a mouse and ran to Ganesha. Ganesha suddenly jumped onto the mouse and seated on him. Unable to bear the weight, Gajamukh accepted defeat. Ganesha announced that he would be his vehicle, and Gajamukh was happy with the decision. He became Ganesha’s friend and constant companion.
Many of us will be wondering why such a tiny rodent is chosen as gigantic Ganesha’s vehicle. But the interpretation is that mouse, which is a destructor (a type of obstacle) by its very nature, signifies evil desires. Ganesha subdued this and became victorious by taming it.