I second @Matthew Dave answer: if that's the story you want to tell, you definetely should.
As for examples of this happening...
Several spoilers ahead:
Martin's Song of Ice and Fire
Oberyn's Martell and Sandor Cleagane mutually destroy each other, even if death does not occur at the same time. It's relevant to our discussion, though: Oberyn manages to hit several times with his poisoned spear, sentencing Cleagane to death, but due to his distraction (or rather, his desire to make the enemy confess his crimes) Clegane manages to crush him before fainting.
This, of course, isn't equal to your idea of the hero deciding to spare his enemy, but the "distraction" theme is present.
Sanderson's Mistborn saga:
In the third book, Vin understand that she can destroy Ruin, but this will require her sacrifice. So they destroy each other.
Tolkien's Lord of the Ring:
One example is in the first book, when Gandalf faces the Balrog. In the cinema adaptation, the wizard manages to make the Balrog fall from the bridge, but the Balrog manages to catch his leg with the whip in a moment of distraction. The fall eventually kills both.
Another related episode is in the last book: Frodo and Sam destroy the One Ring (and thus Sauron) but they nearly die on Mount Doom. Even if they eventually get saved by the eagles, Frodo has being tainted by the ring and cannot enjoy simple life in the Shire anymore, and has to sail from the Grey Havens to the Elven lands (that can be seen as an exile or afterlife of sorts). It's heavily implied, anyway, that the whole journey has taken an heavy toll on the hobbit protagonist.
Rowling's Harry Potter Saga
Another vaguely related example: Harry Potter does die in the last book, only to kill Voldemort later.
He and the dragons kill each other in the end of the saga.
What I'm having trouble finding is the exact situation you've described, the whole "the hero forgives the enemy, the enemy strikes, and then the hero strikes back".
To me, however, it does sounds like a common trope, so I'm pretty sure I've seen it around somewhere
E.g., in the Dragonball Z anime,
Goku manages to reduce Freezer to a near-death state, but Freezer asks for mercy. Goku accepts - gifting him some of his own energy, which Freezer immediately use to stab him in the back.
In this example, though, Goku is able to react and kills his enemy outright, but he eventually gets caught in the explosion of the whole planet (if I remember correctly)
On a personal note, if the general idea you want to convey is "Good cannot thrive without evil and evil cannot exist without good", I would avoid the whole "the hero gets tricked" point.
If your hero dies because he showed mercy, it may feel cheap to the reader.
At least, I would feel his death as less important, since it stems from a mistake - rather that the natural climax of the narrative plot.
The problem with black and white ethics is that they may seem a little unbelievable in a real context, if your targeting an audience of "oldest" younger adults or older people still. After all, is it really a good thing to let the evil antagonist go with his life?
It would be more significant - again, in my opinion - if the hero died by the received wounds, or during the fight; after all he fought well knowing the risks and the eventual cost.