Assalaamu alaykum. If a student gives a wrong answer when his teacher asks him a question (about say Chemistry), then is the teacher sinful if he calls the student ''a donkey'' (for giving a somewhat stupid and erroneous answer)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger. 

It is inappropriate for the believer to insult and verbally abuse others. The Prophet said, "Verbally abusing the Muslim is an evil and fighting him is an act of disbelief." [Al-Bukhari and Muslim]

An-Nawawi commented on the hadeeth, saying, "It is impermissible for the Muslim to verbally abuse his fellow Muslims wrongfully according to the consensus of the Muslim nation, and the doer is declared a faasiq (an evil doer and dissolute) as advised by the Prophet ." [Sharh Saheeh Muslim]

Hence, it is impermissible for the teacher to call the student "a donkey" or the like when he gives the wrong answer to a question. In fact, it is worthier for the teacher to be a role model for his students. Moreover, using this approach with the students harms them and does not benefit them at all.

Allaah knows best.