Is one allowed to turn off the stove burner on yom tov while cooking to prevent the food being burnt?
If it is possible to take the food off the fire, and to heat it up later on the same or different fire, it would not be permitted to turn off a burner on Yom Tov. Likewise, if the fire needs to be turned off altogether, this is not permitted of course, and rather the pot has to be taken off the fire.
However, if the food still needs to be cooked, but on a lower flame, and this cannot be achieved by means of taking the food off the fire and replacing it later, then this is permitted.
See Shulchan Aruch and Rema 514:1, and Mishnah Berurah.
If a smaller fire can be lit (by means of transferring the flame), and the pot transferred to the small fire, the Magen Avraham writes that this must be done rather than lower the flame, and this is cited by the Mishnah Berurah.
However, the great majority of authorities do not cite this ruling (see Shulchan Aruch HaRav 514:4; Chayei Adam 95:3; Aruch HaShulchan), and the Taz (502:3) likewise implies that this is not required. This is likewise ruled by Shut Chelkas Yaakov (1:60) who writes that the custom is to be lenient, and this is also the ruling of Rav Moshe (Iggros Moshe 4:103) who writes that “there is no source at all for the Magen Avraham.”
Therefore, if taking the pot off the flame is not an option, it is permitted to lower the flame – but only for the purpose of preparing the food, and not for saving the pot etc.