Fill up the dispensers with TNT and press the button. I have set up the dispensers so that the TNT that launches has the highest fuse possible. The water dispensers prevent the TNT from doing damage, but you can disconnect this from happening ( and destroying it from ever working again) by breaking the redstone that goes underground. Took quite the fine-tuning.

Additional Notes

TNT cannon might self-destruct if the launcher cannon has more TNT in it that the "firepower" dispensers, IE the "firepower" dispensers are empty and the launcher still drops some.