Glad you asked...
The fastest way to kill a Banana Tree is to chop it down with and axe or handsaw. Once you chop it down youn need ton use kerosene and broad-spectrum herbicide. Check out this website on how to Kill A Banana Tree. http://www.ehow.com/how_5511051_kill-ban...
Then again, this answer might help you...
Killing banana trees isn't an easy task. It seems that because they are a bulb and not an actual tree they have to be forcibly dug from the ground. If the banana is a particularly tall one or bothersome it is possible to advertise in the classifieds to see if someone else wants it.

