Learn Farsi: من برای این اشتباه خودم را تنبیه می‌کنم.

The word خود means 'self'. To say 'myself', you add the first-person singular ending -م to get خودم. Because 'myself' is the direct object receiving the action of the verb (it answers 'who is being punished?'), we must add the direct object marker را right after it, making it خودم را.

Why does خودم را come after the phrase for 'for this mistake'?

In Farsi, the standard word order places the verb at the very end. The direct object with را (here, خودم را) usually comes right before the verb or the verb phrase. Prepositional phrases like برای این اشتباه (for this mistake) often come earlier in the sentence, right after the subject.

What makes up the verb تنبیه می‌کنم?

It is a compound verb from the infinitive تنبیه کردن (to punish). تنبیه means 'punishment' or 'discipline'. To say 'I punish', you conjugate the کردن (to do) part. You add the prefix می‌ for the present continuous/habitual tense, the present stem کن, and the 'I' ending -م, giving you تنبیه می‌کنم (literally 'I do punishment').

We already have the 'I' ending on the verb and on خودم. Do we have to use من at the beginning?

No, you can drop من. Because the verb ending -م and the reflexive pronoun clearly show who is speaking, saying without the subject pronoun is perfectly natural and common. Using here just adds a little extra emphasis to the subject 'I'.