Is cutting off a verse or not completing it considered disbelief, and what is the ruling on doing so in Quran teaching lessons with the intention of teaching, especially if the teacher recites part of a verse or from its middle?

The assertion that one must recite or write the entire verse when quoting it, rather than just the relevant part, is incorrect and contrary to the practice of scholars.

If anyone has indeed made such a claim, its meaning cannot be taken in its absolute sense. Rather, it likely refers to a "hideous stop" (Waqf Qabih) that alters the meaning, such as stopping at "Know that there is no god" without completing the verse. This corrupts the meaning and changes the intended sense, and whoever intentionally does so, meaning to convey that corrupted sense, has committed disbelief.

There are other forms and instances of hideous stops that corrupt the meaning of speech. These include stopping at "Certainly those have disbelieved who said" and then starting with "Indeed, Allah is the Messiah, son of Mary," or stopping at a negation without its affirmation, such as "There is no god."

However, if a reciter is forced to stop due to breath, it is permissible for them to do so, then they should return to what preceded it and connect it with what follows.