In Section 89 of the Doctrine and Covenants the lord says meat is to be used sparingly. Church members are counseled to not to waste flesh when they hunt (however the decision to hunt or fish is a private one). Members are also free to choose vegetarian diets if they wish, however, vegetarianism is not specifically counseled and is not understood to be scripturally mandated, and teaching otherwise is an apostate practice.
Paul, in a letter to Timothy, describing future apostate, spoke of how there would be those "commanding to abstain from meats" (1 Timothy 4:3). Section 49 of the Doctrine and Covenants says that those that preach abstinence from meat are not ordained of God and that he has ordained the animals for the use of man for food and for clothing.
However, while animals are provided for man's use, it is not understood that we are commanded to use them.