I have no connection, which means I don't need to be here. So I'm leaving — no matter what anyone says!
Literal
I [topic-は] relation not-exist, equals, not-exist-[even if-ても] fine. So, here [from-から] leave whatever [quotative-と] say-passive-[volitional-よう][even if-とも]!
Dramatic/emotional monologue. イコール 'equals' is an English loanword used metaphorically to signal 'which means, that is to say' — an unusual colloquial bridge between clauses. いなくていい 'don't need to be (here)' is the ~なくていい pattern applied to いる 'to exist/be present.' 出ていく is a compound verb literally 'go out-and-leave,' stronger than simply 出る. 何と言われようとも uses the volitional + とも pattern 'no matter what is said' — classical/literary but productive in emphatic speech.