I didn't address the first quote because it doesn't contain the word "exterminate." If we were arguing that these passages support the death penalty for heresy, then there'd be no argument. It's clear that's what they say. But you didn't write, "Thomas Aquinas supported the death penalty for heresy." You wrote that Thomas Aquinas used the word "exterminate" to mean "kill" and used these quotations to support your assertion; however the example you chose demonstrates the opposite of your argument, that he had to expand on the word "exterminate" to get the meaning across. Your first example, that you've reposted here, reinforces this understanding; this time the word used is "to sever." Again, he has to expand on the word; severed from what? Not from the Church, not from society, but "from the world, by death."
If it is ever necessary for you to hire an Exterminator because of a bug or rodent problem be certain the exterminator is fully aware you don't want the problem solved by "killing" those creatures. You simply want them moved to your neighbor's house.