Several questions about trimming the yellowed leaves.

Older links at the top of the thread seem mostly not working now, so a new one for talkin' purposes:

Tall Yucca

Assuming your plant looks something like the one above, it likely started out as more like Short Yucca.

The "trunk" in the taller picture is the result of trimming off the lower leaves as they yellow and die, much in the same fashion as for a palm tree. Some varieties don't "stalk up" in this manner, but the more common ones sold as ornamental plants usually do if they survive long enough. (The transition from "bushy" to "tree-like" can take several decades with some varieties, so I will decline to argue the behaviour of the various varieties.)

The flower stalk, as on this Bloomin' Yucca is a different matter. It can be trimmed back after the flowers fade, but usually (on the ones in my yard) will fall off without your assistance, so it's a matter of how neat you want to keep the #@$! things.

As a general rule, leaves that yellow or otherwise look unhealthy should be removed from most plants, as they may be infected with "something" or, if left to rot in place can be a breeding place for "something else" unpleasant that you don't have - - yet. Yucca isn't much different than the general run of plants in this respect, except that one that has started to produce a pretty(?) central basal stalk can be made a lot neater with regular removal of the old leaves as they fade.

As with most desert plants, overwatering is probably the most common cause of poor plant health although yucca are somewhat more tolerant than some cacti. Even very minimal amounts of fertilizer can kill many kinds of desert plants. Local advice from someone who can determine the specific variety should be sought before ever adding even "just a bit of fertilizer," unless you're inclined to serious experimenting and prepared to compensate for mistakes (which is, after all, one of the joys of exotic plants).

Getting rid of an outdoor yucca can be difficult. Total neglect doesn't work. Even prairie fires don't seem to have much effect. The suggestion would be to chop off as much of the plant as possible and immediately, while the cut surface is still wet with sap, paint the cut ends of the stump with an approved "brush killer." (One marked for poison ivy control probably would have appropriate ingredients, and is available almost everywhere in the US, although the "approved ingredients" may vary with the state.) This is the method reportedly used by several state "highway weed control departments" in the US, although I haven't seen specific results on effectiveness on yucca. (Some "weeds," notably red cedar, often require repeat treatments for two or more years with this method.)

John