。
I'm not stupid enough to do something like that.
Literal
I [topic-は] such thing [object-を] do-like idiot is-not.
The structure [verb]+ような+noun creates a relative clause meaning 'the kind of noun that [verb]s' — here 'the kind of idiot who does something like that.' そんなこと picks out an unspecified 'that sort of thing' known from context. 馬鹿ではない negates the identity assertion cleanly.