If you enjoyed Fallout 76's mutation system but you preferred Bethesda's singleplayer take on the post-apocalypse, then you might want to check out a new mod called FO76 Style Mutations. It adds most of Fallout 76's mutations into Fallout: New Vegas, complete with all their relevant buffs and debuffs.
With the mod installed, you pick up mutations either by exposing yourself to radiation—the higher the dose, the more likely you'll mutate—or by injecting yourself with serums. You can buy serums from doctors or craft them yourself if you have a Science skill of 100.
Every mutation has both an upside and downside, and most of them are the same as in Fallout 76. Some of them are tweaked: for example Talons, which boosts unarmed damage, dampens your Repair skill, whereas in Fallout 76 it harmed your agility. You can view all the mutations' modifiers on the mod's Nexus page, and the mod adds a new trait that you can pick at the start of a playthrough that reduces the negative impacts of mutations.
All of Fallout 76's mutations are there except for Carnivore, Herbivore, and Plague Walker, which the mod's author Hopper31 says "either proved extremely difficult to implement, or lacked an equivalent prerequisite to function".
You can remove mutations either via RadAway, which has a chance to remove a random mutation with every use, or a new item called Mutate-Away, which is guaranteed to remove a random mutation. Rad-X will suppress all the effects of mutations temporarily.
Lastly, you can lock your mutations using the re-usable Gene Starcher, sold by Dr Usanagi.