Don't butt in on our conversation.

Literal

We [of-の] talk [of-の] obstruction [object-を] don't-do [emphasis-よ].

邪魔をする literally 'to do obstruction' = 'to bother, to interfere with.' The negative imperative な combined with よ creates a direct but not overly harsh prohibition. Classic casual masculine speech — 'knock it off!'