OTOH, if TA used "to exterminate" to mean "to drive out," the sentence would read "...to be driven out thereby from the world by death." If I'd never heard the word exterminate before, this second interpretation is the one I'd conjecture from the context.
In the event you still question how Aquinas thought "heretics" should be treated I'll post the one you keep forgetting:
Aquinas.: SMT SS Q[11] A[3] Body Para. 1/2
I answer that, With regard to heretics two points must be observed: one, on their own side; the other, on the side of the Church. On their own side there is the sin, whereby they deserve not only to be separated from the Church by excommunication, but also to be severed from the world by death. For it is a much graver matter to corrupt the faith which quickens the soul, than to forge money, which supports temporal life. Wherefore if forgers of money and other evil-doers are forthwith condemned to death by the secular authority, much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death.
Perhaps you should study what Aquinas meant by "put to death." and "severed from the world by death."
Do you suppose he meant to kill them and then ship their bodies elsewhere?