It's fairly clear that the idea is that one Wolverine has killed the other. The "twist" from the cover shot (showing what appears to be two Logans fighting) is that it was actually voluntary.
We know from past comics that Logan can regenerate from appalling damage, up to and including his whole body being blown apart but we also know that damage to his brain is irreversible, something that was a key point in the film X-Men Origins: Wolverine.
It therefore follows that if one Logan could somehow cancause massive damage to both his alter's heart and brain you'd stand a fair chance of killing the otherthem, or at the very least leaving them a complete vegetable.