At the current build the mutants stay alive and well after vivisection but there really isn’t any point in it. My suggestion is that after the mutant is done with this invasive prosedure it will be gone from containment and you will get the mutated DNA automatically.
There could also be a marker if you already have researched the captive mutant. Personally I don’t always remember which worms I have researched and closing the window and checking Phoenixpedia just takes extra time.