The only iffy part is whether throat slicer is allowed by a participant in a grapple as opposed to someone outside it - as written it is its own standard action, and grapple only allows a restricted list. Thematically that's when it's supposed to work, inside a grapple, but I dunno.
You might expect the big bad to do something about the grapple on their action between those two of course.
So the Sorcerer "threw" (Telekinetic Charge) the Brawler at the Big Bad and the Brawler had Grab. So this all actually happened in one round. But could've happened as I described and, then, yeah, the Big Bad would've had one round to break the grapple. I guess Spellcasters can take out enemies in a single round, too... maybe this is fair/equitable.