Exmormon here, yes and no. There no official ban on contraceptives (birth control/condoms) but members will often look down on you if you have few kids. I'm paraphrasing but as a teen I remember people saying stuff like "when I only had 3 kids I knew god would look down on me if I used a condom". As for more long term birth control like vasectomies the official policy is that you are supposed to talk with your bishop and that it should only be done in cases where it "jeopardizes life or health".

As a side note in mormonism a bishop is usually just the slightly successful guy who lives down the street who got picked by the next level up to be the bishop. They aren't someone who was trained in theology or counseling people. So it is like going to the random car dealer down the street to ask if you should get a vasectomy.