Get them out of the water. Cut off the rotting bits and remove the dead tops. Then pot them up into a growing medium and give them a lot more light. They are etiolated and lack of light could be why the tops are dying. Be aware that outdoors mint naturally more or less dies down to the ground, depending on your winters. It is difficult to keep mint growing indoors in winter unless you can provide cool temps and a great deal of light.

I started a discussion about rooting things in water but I have no experience with mint at all, in a pot, ground, or snippings in water. Didn't want it to seem like I was ignoring your discussion.

Hi! I have been rooting mint from freshly cut stems all summer this year for the first time as well. It works like a charm. I cant stop doing it, just too much fun. Occasionally some stems dont make it: they take a long time and rot before growing roots. For me MANY root as soon as 48 hours. No kidding. I would try again with some new cuttings. Where did you get those stems from? I dont actually know anything about growing mint indoors, never done it. I sat the jars on a bright window sill, but less that one hour of direct sun.

Have grown the mint in a pot of soil and not in water. It turns around so good.

@allyssa macallister I potted into soil several mint stems that I had rooted in water and I was thinking a little bit about what you had written. I noticed several things: When the cuttings were taken from plants that were healthy and growing vigorously the cuttings rooted quickly and copiously. Even when a plant is healthy a stem that is growing strongly will root better than a stem that is 'old' and not growing that vigorously. And stems from a plant that is declining may die without rooting. Four stems out of five I took from a mint plant that is waning died within 48 hours of putting in water. That really surprised me. But I had never taken cuttings from an ailing plant before this. Maybe some of the trouble you are facing is because you are not starting with healthy enough cuttings. It will work for you. Mint is very easy to grow but even mint, I guess, has some limitations. Like Floral said, some bright light is necessary also.

And something else I learned from an Yter might be quite true. The roots on the cutting incubating in water are used to surviving in an aqueous medium. When you then plant them in soil they have to learn to survive in soil and stay alive too. The transition can be very stressful. So it may not be a good idea to wait too long for really long roots. Some roots and short roots are OK. Nascent root tissue may make the transition more easily. My experience is minimal. I have only rooted thyme, mint and basil in water and then potted them. Cuttings with 2 to 3 mm roots had no trouble transitioning to soil. But all these three plants root easily. Also for a few days ( 2 or 3 days) keep the soil wet but drained, then only just moist. That will help the transition as well. All said and done a sickly cutting that has some roots may not be able to make the transition to soil.

Start with strong healthy cuttings, especially when you are a beginner.

Good Luck :)