Learn Russian: Не надо винить себя, это не твоя ошибка. - No need to blame yourself, it is not your mistake.

Себя is the reflexive pronoun meaning "oneself" (here translated as "yourself"). In Russian, when the person doing the action is the same as the person receiving it, you must use себя. Here, it is in the accusative case because it is the direct object of винить (to blame).

Does себя change if I want to say "I shouldn't blame myself" instead of "yourself"?

No! A great thing about себя is that it doesn't change based on person, gender, or number. It translates to myself, yourself, himself, themselves, etc., depending on who is performing the action. "I shouldn't blame myself" would be Мне не надо винить себя. Себя only changes its ending for grammatical cases, not for who is acting.

Why doesn't this sentence start with Ты (You) or Тебе (To you)?

Не надо is an impersonal expression meaning "there is no need" or "one shouldn't." You could add the dative pronoun and say Тебе не надо винить себя (You don't need to blame yourself), but leaving it out makes it a more general, softer statement, just like "No need to blame yourself" in English.

Why is it твоя ошибка instead of твой ошибка?