The subordinate (relative) clause is "I know who has committed the mistake. " The noun clause (underlined) is the direct object of "know". The case of the relative pronoun is governed by its position in the subordinate (noun) clause.
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JohnBoz Using "committed" makes the mistake sound like it was a crime or somebody died. "make a mistake" is natural.John; That's true, but the poster was asking about "who" versus "whom".
Tonny LeeWho is used for people you have known before.Whom is used for people you have not known before.No, that's not the point at all. "Who" is used as a subject and "whom" is used as an object.
mrmanshubhamHe is the man whom (I know) has"I know" is parenthetical. "The man has made the mistake" is the main idea. (I know that) he has made the mistake.committedmade the mistake. ... there should be who instead of whom but I could not understand the logic behind it.