This is definitely the Huntsman series by Douglas Hill. I only have books one and three of the series, but I've been able to find matches for several of your points.
In the first book we are told the Slavers have come to Earth to mine it:
One things he failed to learn was the origin of the Slavers – what other world they came from. But to Finn, who knew nothing of space travel or other planets, it was a meaningless question. He was far more interested in something Baer had found out – what it was that had brought the Slavers to Earth.
“They’re dead set on metals,” Baer told him. It seemed that most of the smaller Slaver bases were built on or near some source of special metals, left from the Forgotten Time. Not natural ores, but metal that had been worked, or created, by the ancient humans who had built that glittering and unnatural civilization, and then had destroyed it.
“There’s lots of that stuff around,” Baer went on, “only the wilds’ve covered it, an’ you gotta dig some to get at it. That’s what the Slavers do, a lotta the time – dig. Usin’ their machines, or their slaves, or both.”
Destroying the base with a USAF missile happens at the end of the first book:
Silently he moved round the vault, peering at the cases, squeezing behind them to examine the metal walls, by touch more than sight. The cases themselves were mysteries, even when a stray moonbeam slanted in from the tunnel mouth and spotlighted a printed word, faintly visible on the outside of one case – USAF.
It was not a word that held meaning for Finn. Nor did the contents of one of the cases, whose lid he found loosened by corrosion. Long, heavy, cylindrical objects of dark metal, with other odd words printed on them. What, he wondered idly, had ‘Thermal Grenade Launcher’ meant to the men of the distant past?
Finn was never to know precisely what had been stored in the vault, in those cases marked USAF. But there was no doubt his wish – that they held some kind of weapon – was answered.
The half-melted case erupted in a volcanic blast of light and fire.
The shock of the explosion hurled Finn backwards, deeper into the tunnel, and flung the Bloodkin and Slavers in tangled heaps across the floor of the vault.
And then they vanished, into crushing blackness.
The force of the explosion finished the job that time had begun on the weakened metal of the vault. In a thunderous, bellowing cascade, the entire vault collapsed inward, burying Bloodkin and Slavers alike under tons of earth and ruptured metal.
The reference to the slavers calling humans rats is in the third book:
So, Finn realized, no matter what he said or did, Cacinnix would always see him and other humans as little rats. Little verminous creatures, to be captured, put to work, tormented, experimented on and casually killed, without a second thought.
The alien was turning away, still talking in that idle manner, as if to himself. But now the words were like ice-cold steel, stabbing into Finn.
“That will do for now,” the alien was saying. “There are other duties to attend to before the night’s rest. Tomorrow, I will spend the day with little Finn, make him speak some more, learn all that I can about him. And then perhaps I will cut him open, and see if he is formed differently from other rats.”
In the penultimate chapter of the last book the main protagonist Finn fights the slaver Cacinnix. Finn loses and is about to be killed when Cacinnix suffocates because the air is too dry:
The great head swung, and the purple-black eyes fixed on to the gaping hole where the grating on the ventilation tunnel had been.
“No!” Cacinnix croaked again, fear and fury in his gobbling voice. Twitching, staggering, the alien raised one vast foot, to bring it crushingly down on Finn, where he lay dazed and gasping.
But that final, vengeful attack was not completed. The monster tried to cry out, but the sound was only a grating, wheezing rasp. And then Cacinnix swayed, and stumbled – and toppled backwards like a felled tree.
For a moment more, the huge hands scrabbled feebly at the wrinkled throat. But then they fell away, limp and lifeless. And the deep purple-black of the eyes faded, until finally they were as blank and colourless as glass.
Baer moved painfully and warily forward, finding his machete, then peering down at the giant corpse. “Choked to death,” he said wonderingly. “Sure musta needed that cold wet air.
And after Cacinnix is killed the aliens leave Earth for good.
I cannot find a mention of the part machine/part animal drones, or of a human being stuffed, but those plot elements might be in the second book, which I don't have.