When the female assassin pulls the trigger, this rifle fires backwards and mortally wounds her.
I understand George Clooney is a highly skilled gunsmith, but is it possible to reverse a rifle mechanism in such a dramatic way?
Yes, but not to literally fire a bullet backwards. Instead they might be able to fire the guts of the gun into the shooter's face. With some guns that's plausible, but it turns out that's very difficult with the rifle used: the Ruger Mini-14.
Firing the bolt into the shooter's face?
Most rifles have a heavy cylinder of metal (the bolt) holding back an explosion (the powder charge) right in front of the shooter's face which unlocks with split second timing. With certain rifles if things go very wrong that bolt can wind up flying into the shooter's face. Those are rifles where you remove the bolt out the rear of the gun.
Rifles normally have multiple safety mechanisms and design elements preventing this from happening, but gunsmith may be able to disable these mechanisms and set up conditions so the gun will catastrophically fail.
The Infamous Ross Rifle
This is just what is supposed to have happened with the Ross Rifle.
The Canadian WWI era Ross Rifle is widely considered to be one of the worst military rifles in history. There's a persistent story that if you assemble the Ross Rifle incorrectly the bolt will come flying out the back and smack the shooter in the face. Some professional gunsmiths decided to try and replicate that. The results are educational.
Here's a discussion and demonstration. The disassembled it incorrectly, disabled a few safety features, and fired it. You can see it in slo-mo at 13:40. And it still managed to stop the bolt! They discuss what stopped it at 14:30.
Even though they couldn't manage it, they were limiting themselves to simulate a situation that might reasonably come up in the field. It's totally plausible a malicious gunsmith could deliberately modify such a rifle to cause the bolt to fly out the back and kill the shooter... if the shooter didn't inspect the rifle too closely.
But not the rifle in The American.
The Ruger Mini-14
I haven't seen The American, so I don't know what exactly happens, but the rifle in question is a Ruger Mini-14 that's been around since the 70s. Its basically a scaled down M1 Garand of WWII vintage. It's a semi-automatic, gas-operated, rotating-bolt rifle. It is extremely reliable.
As we said, in many rifles the bolt is designed to exit the rear of the gun, and the safeties to prevent this can be circumvented. But not the Ruger Mini-14.
The barrel and receiver are basically one big chunk of metal. The bolt comes out the front of the receiver for disassembly, as seen in this disassembly video. Behind the bolt is a very, very solid piece of metal.
I don't see how a gunsmith could modify the Ruger Mini-14 to have the bolt or anything else reliably fly into the shooter's fact without the shooter noticing the gun had been heavily modified.
What is plausible?
What George Clooney's character could have done is cause the chamber to blow out through a combination of weakening the lugs keeping the bolt locked in place, a barrel obstruction to increase the pressure on the chamber (hidden by his custom suppressor), and using an hot round with more than the normal amount of gunpowder to create over pressure in the barrel.
When she fired the round the excessive gases from the hot round would be momentarily blocked by the barrel obstruction building up pressure in the chamber. Unlike a vintage 1860 repeater made of weaker bronze or brass, a modern rifle with modern safeties made with modern metals is very unlikely to shatter under pressure. Instead, the weakened bolt lugs would fail and the chamber pressure would vent backwards into the shooter's face.
Not in a dramatic "bullet through the eye socket" or "hunk of metal lodged in the brain" sort of way. It would send small parts, bits of sheered lugs, plus the shell casing, flying backwards. Probably not large enough or fast enough to be reliably fatal, though I wouldn't want to be anywhere near it. The bolt would remain inside the receiver.
Not unlike what happens to the Ross Rifle. And as you can see, the ballistic gel behind the rifle is hardly scratched.
The much larger effect would be the shock, flash, and noise dazing the shooter. She's not wearing eye protection, so she might get shrapnel in her eyes. She's not wearing ear protection, so she'd definitely have hearing damage and disorientation.
She'd certainly be in no condition to fight back should George Clooney's character decide to finish the job.