Without a picture of the steps and unwanted tree, it is extremely difficult to determine the best way to eliminate it. If you e-mail a picture explicit site specific, instructions can be provided. In the absence of a picture, the following is a possible solution. Cut the tree back so a 6-8 inch portion of the stem/trunk remains. Eliminate any lateral twigs/slash branches. The remainder will be just a stick. Purchase a product containing glyphosate. These products are usually labeled as total vegetation killers, weed and grass killers, or something similar. Mix a solution according to the product label directions. Carefully paint the entire trunk/stem with the mix. Avoid getting the glyphosate solution on any other plant material in the area as it will kill anything green and growing. When doing this, wear gloves and protective clothing according to the label cautions. The glyphosate should translocate to the roots of the tree and kill the tree, roots and all. This will take at least seven days. If after this time, the tree appears to still be alive, repeat the process. Once dead, cut the remaining stem to the ground. You may wish to tie a ribbon or something similar to the stem while the glyphosate is active on the tree, so it won’t become a hazard to those using the steps.

Source: OSU Extension Service