Real Dictionary

tut
Tut is used in writing to represent the sound that you make with your tongue touching the top of your mouth when you want to indicate disapproval, annoyance, or sympathy.
verb: If you tut, you make a sound with your tongue touching the top of your mouth when you want to indicate disapproval, annoyance, or sympathy.

tut in American English
(a sound) used to express impatience, annoyance, mild rebuke, etc.: a click, or sucking sound, made by touching the tongue to the hard palate and rapidly withdrawing it: usually repeated one or more times (tut-tut)
interjection: (used as an exclamation of contempt, disdain, impatience, etc.)
intransitive verb: to utter the exclamation “tut.”
noun: an exclamation of “tut”