For part of Rogue One,
Cassian Andor wants to kill Galen Erso to prevent him from continuing to work on the Death Star. However, Andor has just witnessed the destruction of Jedha City from the Death Star, meaning it was too late for that. Why did he still want to kill Erso after this?
Blind following of orders likely isn't the reason, as he had a chance to check in with his superiors but chose not to.
Why kill someone who no longer posed a threat?
(As a companion to DVK's answer based on the novel, here's an answer sourced only from what's shown in the film.)
Cassian's Orders Are Re-Confirmed
Cassian does check in with his superiors after the destruction at Jedha. He tells them about Jedha and about Galen Erso being at Eadu.General Draven replies with a reiteration of his previous orders — to kill Galen instead of extracting him as a defector.
Even though Draven knows the Death Star is finished, he is concerned about future work that Galen may do for the Empire. He sees him as too dangerous to let live.
Draven says this out loud in the presence of the communication officers who are in contact with Cassian. It's not shown whether the operators pass on the reasoning behind the orders as well as the orders themselves, but either way it's very likely that Cassian understands Draven's reasons quite clearly.
This makes Cassian's later decision to disobey the orders even more significant.
Four reasons, expounded on in official Rogue One novelization by Alexander Freed, all in Chapter 2.
Because he was ordered to by General Draven.
He thought back to his conversation with General Draven in the hangar. The assurances of trust, of confidence in Cassian’s judgment, were swiftly being pulled into the amorphous eddies of his memory, but Draven’s orders were etched in steel:
Galen Erso is vital to the Empire’s weapons program. There will be no “extraction.”
You find him, you kill him. Then and there.
However, you're right, he wasn't JUST blindly following orders. He fully agreed with them, for three more reasons:
Draven wasn’t wrong to want Galen Erso dead. It would be a righteous killing as well as a practical one, ...
The execution was of someone that Cassian saw as guilty for the deaths of civilians.
... the execution of a man surely responsible for the deaths of countless civilians. Erso’s years inside the Imperial war machine could have no innocent outcome.
And, had he not been killed, he could have cost more innocent lives by continuing to work for Empire
If killing Erso saved a single life, then that was cause to celebrate—but if not, his assassination was no less justified.
You claim in the question that "Andor has just witnessed the destruction of Jedha City from the Death Star, meaning it was too late for that" and "someone who no longer posed a threat" - but that's not really a valid assumption. He could have continued to work on Death Star (say, something broke or didn't work right). Or on the next, even worse, project.
And, on top of that, killing him would free Mon Mothma from her quixotic idiocy of trying to follow her futile "present him to the Senate" plan
Nor did the contradiction between Mon Mothma’s orders and those of General Draven trouble Cassian. The notion of bringing Galen Erso to a Senate hearing—of exposing the Empire’s planet killer, of creating such an uproar inside the civilian government that the Senate would move openly against the Galactic Emperor—was absurd on the face of it.
Mothma desired a leveraged détente—a political solution made possible through rebel military action—that was, to Draven and Cassian, self-evidently impossible. The Imperial military was loyal to its commanders, and its commanders believed that they, rather than the Senate, already effected complete control over the Empire. They were right. No peaceful transfer of power could occur.
Yet Mothma was an idealist. Cassian suspected she wanted a Senate hearing not because she thought it would work, but because she felt obligated to try. Cassian admired Mothma. Galen Erso’s assassination would free her from the obligation of a doomed peace effort.
Legends sheds a bit of light here. Maw Installation was the Legends source of the Death Star. After that, they developed the Sun Crusher, a weapon that could cause a star to go nova, at a fraction of the size of the Death Star.
Could you imagine what else Erso and his team could have developed if they had lived?
