The answer is more complicated than a person would think. The environment does not matter much in any solution, but with some, you will not want any rain for a few days at least.

Dig like a little weasel. Way down there like 47 ft or so and then maybe you got it. Yucca are tubers, so that means that all those little hair-like roots left over are going to try to survive. If a person was to go this route I would suggest using a soil sterilizer. ONLY use these products if you do not plan or have ANY other plants in the area ( 5 feet minimum distance from sterilized area). results with this method are mixed depending on weather, application method. and so on. Any way you go about it this one is a lot of physical labor.

One method suggested was similar to the first, but do not dig so deep and do sterilize the soil – after tilling at a medium depth ( 4-6 in.) then cover area with cardboard or a good quality weed barrier tarp for 1 or 2 seasons. Some people have issues with suckers and starters eventually work their ugly little faces at the edges. This may be easier to get a handle on as the individual will be small and weak.

Cut plant down to the ground or as close as you can get. Use a chain-saw or whatever method is available and easy. The brand name I use is “TORDON”, but the chemical is for killing trees out after they are cut down. Completely saturate the entire stump that remains exposed. This should be done according to manufacturer directions, but avoid water or check about the rain as these type products are NON-SELECTIVE. This means that not only does this kill what it touches it kills everything that comes in contact with it and all that it bleeds on. Like spraying acid in the air over your lawn, potentially. Kill off any new little sprouts as they appear by just pouring a little of the same over the leaves to get a good coat, with the same considerations in mind. If you are careful 1 or 2 seasons should be sufficient.