The first question to answer is "is this actually an issue or just something I personally don't like?" If other moderators are worried that shutting this mod down would result in losing users, then there is a decent possibility that the community may not actually see the actions of this moderator as noise, but rather find them an interesting part of the community. Before taking any action, you should really confirm it is actually a problem and not just something you don't like personally.
I really can't emphasize the importance of this first point enough. One of the most destructive things that can happen in a community is that the leader of the community gets it in their head that the community should move in a different direction than the community wants to. It generally plays out that the leader tries to push in a certain direction against a moderator or officer that most represents what they dislike, they get limited response from other moderators or maybe slight resistance because those other mods see the will of the community but don't want to directly go against the leader because they don't care enough to fight for it. Eventually though, the stress causes a tear in the community and the majority of the community ends up leaving because the leader is seen as out of touch and making it less fun to be around.
You may very well be correct, but you need to be very careful and open minded to the fact you may not be if you aren't getting support from the rest of your team pretty easily.
Assuming that it is actually a problem with the broader community as a whole and only something that certain users like, it is best to clearly document why it is an issue and come up with ideas for how to avoid those issues and find a way to best service the users who will be impacted but also to make sure the community as a whole is restored to where it needs to be. After you have this reasoning, approach the moderator with it and try to work it out with them. If you can make them understand how it is disruptive and provide proof that the community doesn't like the disruption, you may very well be able to get them to alter their behavior.
If they still don't believe you or continue in their behavior, talk to the other moderators and get them to reinforce your case if they agree with it. (Again, if many of them don't agree, it may actually be you who is seeing the situation incorrectly.)
If the moderator continues to go against the entire moderation team and the broader community's wishes, then it may be time to take further action. Perhaps disabling auto-responders in the chatroom or, in extreme cases, removing the moderator may be necessary, but this should really only be a last resort action if they have clearly stopped participating as a member of the team and are off doing their own thing regardless of the wishes of the rest of the team and the community.