Clear away all the undergrowth from under the basjoo banana. You can use your hands for this procedure since you only need to make enough room to work at the base of the tree. Toss any debris you pick up into a wheel-barrow or garden cart.
Cut the outer banana leaves away with your shrub shears. Removing the larger leaves first will expose the stems of the smaller ones. Cut away the tightly wrapped smaller leaves with the hand-held pruners. Save the leaves you remove and add them to your mulch pile.
Remove the banana tree with a pruning saw. Cut the tree at shoulder height, for tall trees, to make the sections easier handle. Then cut the lower section of the trunk as close to the surface of the soil as possible.
Lay a circle of mulch, about 4 feet in diameter and at least 3 inches deep, over the stump. The type of mulch you use should come from an organic source such as pine, cedar or other organic materials. The greater the depth of mulch you use, the greater amount of protection you provide for the remaining tree roots.
Allow the mulch to remain on site until spring and do not water or fertilize the area.