I wanted to know if it is from the sunnah or a part from having good ettiquete as a teacher to tut when a student makes a mistake in memorisation or tajweed?

Question
Assalamu'alaykum wa rahmatulli wa barakatuhu

I wanted to know if it is from the sunnah or a part from having good ettiquette as a teacher to tut when a student makes a mistake in memorisation or tajweed? I have seen some learned teachers in my town do this.

May Allah reward you with goodness in this life and the hereafter.

Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh,
The "tut" also known as "tsk" has a different meaning in different cultures.  In the Arab culture for example, it simply means "no".  It has no negative implications more than saying that. It is accepted by all and not considered impolite. 
 In the Western culture it means a stronger disapproval and even a reprimand and is considered impolite by many.
So, we have to understand that most likely, the teacher is just saying "no, that is not correct" and nothing more since in the Arab culture, that is what it means and most Qur'an teachers are Arab or have been taught by Arabs.
Ameen and May Allah give you the same.