yuccas have hard waxy leaves which repel sprays.
buy a bottle of Gyphosate concentrate (the stuff you dilute with water) and a half-inch paintbrush.
Saw off the "trunk" about a foot above the ground (this saves you having to lie down and you can work from a kneeling position). It looks to me like you have several stems but it will become clearer when you saw it off. it is possible to pull leaves off individually, wearing strong gloves.
Immediately, dab the glyphosate onto the cut surface of the stump while the sap is still running. If the sap washes it away, dab on some more. Check again in half an hour.
the weedkiller will be absorbed into the living fibres and drawn down to the roots, which it will kill. It is inactivated by contact with the soil so it will not poison the ground (and there is no point pouring it onto the ground).
if rain is expected, put a plastic bag or something over the stump to prevent it washing away the glyphosate.
If you get any suckers or shoots, do the same with them. it will take a few weeks for them to die and go brown. If you see any green leaves it is not dead, so cut at the node and apply again.
I did this with a bay tree a couple of years ago. The stump is dead, I got a dozen or so suckers coming up which I cut and treated. I also did a 20-foot yucca with several stems which was easier. Most plants are not so prolific with suckers.
once the cut stump has dried and calloused, it will not absorb the weedkiller.
if it is a yucca or similar, the stem is not woody and will rot away. When you are sure it is dead you can mound it with compost to accelerate the rot.
