Remove the bark from around the tree. Use a hatchet to cut away the bark around the whole circumference of the tree. This is girdling and prevents the vital nutrients that the tree requires from reaching the roots. Within a few weeks, the mayday tree should be dead.
Apply an herbicide made for trees to the mayday tree leaves. Coat the tree leaves with the chemical on a hot, sunny day when there is no chance of rain. Repeat the process as stated on the label of your specific bottle of herbicide.
Drill several holes at least 3 inches deep into the trunk of the mayday tree. Spray herbicide into the freshly drilled holes. This will deliver the chemical directly into the tree. Combine this method with spreading an herbicide on the leaves to speed up the death of the tree. Alternatively, pour coarse salt -- such as rock salt -- into the holes to kill the trees without harsh chemicals.