The Joshua tree is a member of the genus Yucca and, as such, is governed by Nevada Revised Statute 527.063, concerning the "Protection and Preservation of Timbered Lands, Trees and Flora."
As far as digging up a Joshua tree is concerned for either private or commercial (defined as the removal of six or more trees in any one calendar day) use, this is permitted, provided: a) that the tree is located on private land and b) you're in possession of the necessary permit. This permit, which will set you back by the princely sum of $2 per tree, is available from the Nevada Division of Forestry and comes with a free shipping permit* (valid for two weeks). The very helpful gentleman who issues these permits is called and you must call him ahead of time on 702/486-5123 and then go to the office at 4747 Vegas Dr. at the appointed hour to collect your papers.
That's the good news. The not-so-good news is that it's an offense to "remove or possess any Christmas tree, cactus, yucca or branches thereof, or knowingly transport or sell any Christmas tree, cactus, yucca or its branches from any of the lands owned by or under the jurisdiction of the State of Nevada or its counties, or on any reserved or unreserved lands owned by the United States," and if you click on this link to the map of federal lands, you'll see that doesn't leave you a whole lot of options, and that's not counting any state-controlled territory. In fact, Nevada possesses less privately-owned land than any other state, with various government agencies controlling almost 90 percent of all land and if you violate the above-quoted statute, you're guilty of a misdemeanor, so make sure you do your homework and get all the right permits if you're considering bringing home a souvenir tree instead of a t-shirt. The Clark County Assessor Parcel Index Maps may help you figure out if your chosen tree's on private land or not, if you can make head or tail of them. Good luck!
*We're aware of the fact that some states and most countries have restrictions about importing alien plants, or in fact any plants at all, so you should check with your local authorities and those of any other territory you might pass through with your tree to make sure no additional regulations/prohibitions apply.
