If you have noticed that the idol of the Lord Ganesha, you may have seen that one of his teeth is missing. The tusk is broken and as per legend, the same has been attributed to the fact that the same was lost when Ganesha was sitting and writing Mahabharata. As a result, the feather broke, and he broke his tusk and went on working on the legend. It is believed that Lord Ganesha decided that he will not stop once he starts with the process and the broken feather did not deter him.
Some also attribute the same to the fact that Lord Parshuram cut off one of the Ganesha tusks as he did not allow him to meet lord Shiva as he was busy in meditation and prayer.