How does this society try to obliterate each individual's mind and self?
There are numerous examples of the ways Ayn Rand shows the society in Anthem as taking away each person's individuality. Early in the novel, Equality refers to one of his sins: the Transgression of Preference. Citizens of that society were taught that it was an egregious wrong-doing to prefer one anything over the other. This pertains to all facets of life including friends and careers. Even having a preference concerning a partner is discouraged, and the Council instead uses the House of Mating. Babies and children are not allowed to stay with parents to prevent any differences in upbringing that might set someone apart.
One of the most predominate ideas that pertains to destroying individuality, however, is the naming of the citizens. Using a number strips a person of who he or she is at the core. That is why it is so powerful for Equality when he names himself Prometheus.
In the above ways and more, the society in Anthem effectively strips each person of his or her personal choice, desires, and values.
In Anthem, the society has attempted to take away the ability and the desire to think. When Equality 7-2521 finds the tunnel in Chapter I, He and International 4-8818 discuss what they should do about looking at it and inspecting it. Equality 7-2521 wants to go into the tunnel, but International 4-8818 says that it is forbidden. The answers that they each give in response illustrate how the Council has taken away their free-will and their critical thinking skills. Equality 7-2521 argues that "The Council does not know of this hole, so it cannot be forbidden." International 4-8818 answers that "Since the Council does not know of this hole, there can be no law permitting to enter. And everything which is not permitted by law is forbidden." These comments illustrate the dependence which the Council has instilled upon its citizens toward their rules. They have succeeded in squelching International 4-8818's desire to think, but they have not had the same success against Equality 7-2521's mind.
In Anthem, the society seeks to destroy the mind through four general paths:
1) They destroy the concept of the individual, allowing only "we" to be spoken.
2) They hold all property and concepts in common.
3) They insist on control of all new inventions and ideas (through production and education, including making private thought a sin).
4) They review all (economic) activity to make sure it is properly focused for the society.