You could either run the master outputs of the mixer through a soundcard with Breakaway and just use the soundcard’s output to send to whatever you’re plugging int. That’s probably easiest.
or… you might be able to modify your external mixer (if it’s analog) to patch Breakaway (using a soundcard & computer of course) into your mixer’s routing…. if you know enough about electronics, how to read schematics, and ofc soldering & desoldering. then you could have Breakaway in the routing of the mixer itself. I’m not sure how useful that would be though, as you would need a mixer with some decent routing options already (think A&H Xone 464), and you would need a good reason to mod your mixer if it didn’t already support whatever routing options you need.
that’s about as basic info as i can provide, without knowing your existing routing, what mixer you have, what audio converter you have, how you’re outputting from tractor (routing), etc.