Why did Voldemort choose to kill half-bloods first over Muggles?

Question

If half-bloods were filthy scum, according to Voldemort, I don't have words to describe Muggles. Why didn't Voldemort choose to eliminate Muggles first which would have been very easy? Also, destruction of entire Muggle gene pool would have removed the possibility of birth of half-bloods.

Answer 1

Revealing magic to Muggles would cause international response.

Though the Dark Lord only had widely targeted Mudbloods for imprisonment and killing, some Muggles were killed under the Dark Lord’s reign. Killing Muggles became sort of like a sport for his supporters, who were allowed the freedom to kill them without being charged.

“Meanwhile, in Gaddley, a Muggle family of five has been found dead in their home. Muggle authorities are attributing the deaths to a gas leak, but members of the Order of the Phoenix inform me that it was the Killing Curse – more evidence, as if it were needed, of the fact that Muggle slaughter is becoming little more than a recreational sport under the new regime.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 22 (The Deathly Hallows)}}

However, though they kill Muggles, they don’t reveal the existence of magic to them. Avoiding revealing this is likely why they didn’t round up and kill larger numbers of Muggles.

“Muggles remain ignorant of the source of their suffering as they continue to sustain heavy casualties,’ said Kingsley.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 22 (The Deathly Hallows)}}

The International Confederation of Wizards was responsible for monitoring violations of the Statute, and had the power to reprimand any country’s Ministry if that Ministry allowed the Statute to be broken through their actions. They hold the Ministries responsible for making sure the Statute is upheld within their countries, and seem to have the authority to do whatever needed to enforce it.

“Adequate security measures were not enforced until the International Statute of Wizarding Secrecy of 1692 made every Ministry of Magic directly responsible for the consequences of magical sports played within their territories.”
_{^{- Quidditch Through the Ages}}

They have the ability to step in if the Ministry mishandles both the sports or creatures they’re responsible for, so this almost certainly applies to other violations of the Statute.

“Each wizarding governing body will be responsible for the concealment, care, and control of all magical beasts, beings, and spirits dwelling within its territory’s borders. Should any such creature cause harm to, or draw the notice of, the Muggle community, that nation’s wizarding governing body will be subject to discipline by the International Confederation of Wizards.”
_{^{- Fantastic Beasts and Where to Find Them}}

The International Confederation of Wizards would be quite a hindrance to the Dark Lord at that point if they were to get involved. They’re not solely political, they’re also able to send teams in to deal with the problem. When the Peruvian Vipertooth kept attracting Muggle notice, they send in exterminators to reduce the numbers. They had wizards trained enough to kill dragons, and could send wizards from multiple countries to overwhelm the Dark Lord’s forces.

“The Vipertooth will feed readily on goats and cows, but has such a liking for humans that the International Confederation of Wizards was forced to send in exterminators in the late nineteenth century to reduce Vipertooth numbers, which had been increasing with alarming rapidity.”
_{^{- Fantastic Beasts and Where to Find Them}}

The hearings of and subsequent imprisonment and killing of Mudbloods is entirely contained within the wizarding community, so doesn’t attract international attention. They could round up Mudbloods by visible means like requiring them to come in for questioning, since it didn't break the Statute. If the Dark Lord did anything that revealed the existence of magic to Muggles, however, the international community (who still wouldn’t want all wizards to be exposed to Muggles) would start getting involved. As the Dark Lord hadn’t even fully conquered Britain yet, he certainly wouldn’t have wanted wizards from around the world to come in and intervene.

The Dark Lord was targeting Mudbloods, half-bloods were safe.

The Dark Lord did nothing to target half-bloods. He did target Mudbloods, either throwing them in Azkaban or killing them depending on how cooperative they were, but anyone who could prove they had at least one close wizarding relative was spared and allowed to go free.

“Nevertheless, unless you can prove that you have at least one close wizarding relative, you are now deemed to have obtained your magical power illegally and must suffer the punishment.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)}}

This of course includes half-bloods, as all half-bloods have one wizarding parent. Further proof of this is that one wizard in the hearings determining blood status claimed he was a half-blood.

‘No, no, I’m half-blood, I’m half-blood, I tell you! My father was a wizard, he was, look him up, Arkie Alderton, he’s a well-known broomstick designer, look him up, I tell you – get your hands off me, get your hands off –”
_{^{-Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-born Registration Commission)}}

If half-bloods were considered just as bad as Mudbloods, this wouldn’t help him any, and would be a useless thing to bother saying as an attempt to save himself.

Answer 2

You have to understand that going after the muggles first would have been a terrible mistake.

Going after large amount of muggles would have created a major muggle-wizard war. And in that war, modern muggles would have the higher firepower and the higher numbers. The only thing the muggle side would lack is information.

That is why Voldemort had to get 100% of the magical world under his leadership before attempting any kind of major move against muggle societies. Just one single treacherous wizard would have been enough to provide muggles with information about what place to bomb and what materials to use to craft magic-proof combat armors and stuff like that. Attacking the muggles without complete unity would be a suicidal move.

Not to mention, Voldemort's followers were mostly pure blood supremacists, the kind of wizards who think muggles still work with pitchforks and fight with swords, killing isolated muggle civilians was sport but they were not even close to 5% ready for a large scale battle against a muggle military force.

We don't see lot of the battle of Hogwarts in the book since it is from Harry's POV but if we go by the movie, it is quite obvious how immensely inferior the attackers side was in comparison to the defenders: the Order of the Phoenix members were defending key areas and fighting as a team with an instinctual organisation. On the other hand the death eaters were just fighting individually with what seemed to be competition between them for the highest kill count, they made beginner tactical mistakes like moving in clusters in large open areas and falling for the cliche explosive on the bridge trap.

It is quite obvious how unprepared Voldemort's side was about large scale war.