In actual combat it is perfectly possible to have both sides attack and hurt/kill each other.
Depending on the nature of your game, I would say this is acceptable, and even a good mechanic to discourage random button mashing and force the user into more careful thoughts about what they're doing.
Another aspect that ties into this is that just because you've stabbed your opponent isn't always an indicator that they're not going to just stab you right back. Being able to deliver a killing blow without taking one in return is kind of an important factor in real fights.
I was just about to mention this, actually.
The most obvious, and most common, way to deal with the situation in games is that nothing special happens when two attacks collide, they just hit or miss as normal.
Attacks interacting with one another is actually fairly uncommon, and when it does occur, it's more often only in specific scenarios (e.g. weapon attacks in Samurai Shodown can clash with one another - triggering a minigame where the loser is temporarily disarmed - but only if certain requirements are met) rather than a general occurrence.