Mistletoe is a parasite. It lives within the tree and causes a slow death. By slow, I mean years or even decades. The parasite produces a fruit which is what we see. The fruit takes on the look of the tree that it has invaded; it is leafed on Ash and Cottonwood or needled on Pinon or Juniper. The parasite itself will move very slowly through the trees. The fruit, however, is delicious to birds. They eat it, flutter from tree to tree, poop like they know how and spread the parasite.
The only way to get rid of the parasite is to cut off the limb where the fruit develops. If the fruit develops on the main trunk or lead or in a large crotch of the tree, the tree will eventually succumb to the parasite. If you cut off a limb with the parasite, you have to be sure to sterilize your tools with bleach (10%) and water (90%) and wear disposable gloves when handling the limbs otherwise you will spread the parasite.
The only way to try to slow the spread of the parasite is to remove the fruit. The problem here is that the fruit is often in hard to reach places (dang birds!) and like all fruit will come back every season. Also, in removing the fruit, if not done properly, you can spread the parasite. And, in case you needed a reminder of this, birds do not respect property lines. You can remove all of your fruit or even the parasite and if your neighbor has mistletoe, you are likely to get it again.