Summarize this article:

To get rid of cattails, you need to completely remove the root system. Cattails propagate through rhizomes. The rhizomes send out additional roots horizontally, quickly resulting in new plants. Manual removal is most effective if you dig out the rhizomes when cattails are first establishing themselves in a pond.  Dig down below the root system to remove the cattails. Dispose of the cattails. Consider using a backhoe for manual removal if you need to remove a larger amount of cattail stands.

Summary:
Dig up the cattails.