Witcher 3 - Mutagen Transmutor

No, you do not keep the Mutagenerator. According to the Witcher Fandom:

• This item is impossible to transfer to New Game +, thus it's best to collect all the mutagens you need for the mutations you want BEFORE you start New Game +.

Note that there's apparently a bug involving mutagens and New Game +:

• There is an unfixed bug that can cause mutagen multiples to be deleted during the transfer. To be precise, any stack of mutagens in the inventory and the stash is likely to be reduced to 1. Slotted mutagens are not affected by this bug. It is therefore advised to:

  1. Make a distinct game save.
  2. Start the New Game +, and as soon as you can, check your inventory to see whether you are affected by the bug. If you are not, nothing more to do, if you are, continue at the next step.
  3. Reload your previous save game.
  4. Split any mutagen stacks in your inventory to be both in your stash and standard inventory - that way you retain 2 copies of each.
  5. Consider to complete all or all but 4 mutations (completing 4 mutations costs 9+ ability points and grants 2 extra ability slots, completing 8 costs 25+ ability points and grants 3 extra ability slots, completing all costs 49 ability points). Note that this takes a very heavy toll on the amount of available ability points, so completing them all is only advised if NG+ is started at a really high level or when you think you have a powerful enough build to let go of 49 ability points. Completing 8 of 12 mutations only keeps one slot locked, but leaves you with up to 24 extra ability points.
  6. Since red mutagens are much harder to acquire than blue/green mutagens, consider placing greater red mutagens in the 4 mutagen slots regardless of skill synergy, since these slots will not suffer from the bug and their mutagens are transferred properly.