Mom used to say the same thing. So what? It's got nothing to do with me.
Literal
Mother [also-も] same thing saying [past-ていた-reflective-な]. So-what [explanatory-んだ-emphasis-よ]. Me [target-にゃ] relation exist-not.
Rough, rebellious speech. 母ちゃん is a casual/childish word for 'mom' (母 + ちゃん). だからどうしたってんだよ is a confrontational set phrase: 'so what?' — the って here is quotative (short for だからどうしたというんだよ 'even if you say so, so what?'). オレにゃ is dialectal/casual: オレには → オレにゃ. Sounds like a tough teenager or yanki (delinquent).