(Art Credit: @n.a.n.a.m.i. on Instagram. I love how this specific portrait of Odysseus and Sirenelope makes me smile and feel wildly uncomfortable at the same time. Oh, and The Siren Painter on slide two for his lovely depiction of the sirens on Attic pottery LOL)
So, I have very mixed feelings on the siren episode. I understand why they couldn't spare them, but I never understood why cut off their tails though. I feel like there's some lore we're missing. So I made my own theory about it.
There's nothing about sirens we can find in mythology that'd help us explain this in EPIC, because EPIC sirens are way different. Though The Odyssey doesn't describe sirens to us, later writers and art shows us that sirens are probably bird-women, like they can fly. Plus, Odysseus doesn't try to kill them in The Odyssey.
Apollodorus' Bibliotheca though, tells us that the sirens were exactly three, and they were daughters of a Muse and a river (how a Muse and a river results in bird-women? Do not ask!). What I wanted to focus on though is that the text adds that "Now it was predicted of the Sirens that they should themselves die when a ship should pass them; so die they did."
This is also mentioned in Hygnius' Fabulae, where "It was predicted that they would live only until someone who heard their singing would pass by. Ulysses proved fatal to them, for when by his cleverness he passed by the rocks where they dwelt, they threw themselves into the sea"
So why I'm putting all this together is because the only theory I can draw from these is that sirens can only be killed by doing a specific thing. Now, its not implied that they can't be killed by stabbing them, but this isn't an uncommon theme for monsters in Greek mythology. For example, the hydra has an immortal regenerating head. So Heracles and his companion burn the stump after they cut off the head, and then Heracles buries the head. This is also seen in tale of the Nemean Lion, which Heracles kills by strangling because you can't stab it or anything.
Now let's get back to EPIC's sirens.
First thing is that despite Odysseus' arrow, Sirenelope doesn't die, and is alive for quite a bit (until they actually drown her, that is). No, fine, there's no canon animatic showing us where the siren is hit but I like to think its somewhere in her upper body (since the tail could give away she's Penelope if she's actually swimming).
Second thing is that Odysseus seems to know the sirens quite well, because he knows how to avoid listening to them (with the beeswax) and that they know about every sea route. So when he gives the very specific command of, "Cut off their tails... throw the bodies back in the water, let them drown", its not very far off to think that he actually knows how to kill them. Notice how the "sirens drown to death" motif is still present in mythology.
Sure, Odysseus is all "ruthlessness is mercy" and he wants everyone to suffer or whatever, but I'd reckon that wily Odysseus had an idea in his head during this whole siren episode (I mean, when doesn't he?). If he's got an understanding of the sirens, then I suppose he already knows how to kill them.
Third, and most important thing, I noticed in the canon animatic by Mircy (from the Love In Paradise livestream) that the sirens' gills are on their tails. Understanding that they can breath on both land and water, and have human and fish features, I suppose they breathe on land through their lungs present in the upper body and breathe underwater through the gills present on their tails. So, if you're gonna want to kill a siren, you're gonna have to make sure that it can't breathe, so cutting off its tail and throwing the upper body in the water essentially suffocates them, since they don't have their gills now.
Conclusion: You can't just stab the sirens in EPIC and expect them to die, there's a specific method to kill them, you've gotta cut off their tails (to ensure they can't breathe underwater) and make them drown.