Scheduling and managing events using Outlook.com calendar
You can't turn off the responses, or you will be unable to track responses.
If you read through the entire thread, you will find some interesting responses and experiences.
jspears0501 had replied to my question on how to stop receiving email notifications of people responses, quoted here below:
I had the same experience and it was a nightmare. I found this option to work for me.
Go to File – Options – Mail – Tracking and select “Update Tracking information, and then delete responses that don’t contain a comment.”
This will stop you receiving all calendar responses via email but will still track the responses. This way you are not flooded with accepted or rejected invitation responses, and you are still able to see who has responded and their response.
I did this, but it is not working properly, though it's the most promising I've seen so far.
Sometimes it works and sometimes it doesn't but haven't quite figured out why yet.