Mutations in Fallout 76 can be both very beneficial to a character, as well as very problematic if you get an undesirable one. Mutations are in themselves non-permanent effects that will go away when you cure yourself from radiation poisoning, but it is actually possible to make Fallout 76 mutations permanent.
If you want to make your current mutations permanent, all you need is to purchase Starched Genes Perk rank 1 and rank 2. This will prevent all healing sources from removing mutations, so the current mutations are made permanent.
Make sure you get the mutations you really want before doing this tough, since you won't be able to acquire new mutations or remove undesirable ones either after having purchased the perk.
With this perk, all your current mutations are in fact a permanent effect for your character, and you won't have to worry about them again unless you want to change them.