If I stun an enemy unit while I'm defending, can my defending unit kill it?

Yes, your defending unit can kill the stunned enemy unit.

According to Rule 423.1.b, a stunned unit does not contribute its might to damage in the combat damage step, but it must still have damage applied to it equal to, or greater than, its full might value to be killed (Rule 423.1.c).

Here is how the interaction works during a Showdown:

1. Stunning: When you stun the attacking unit, it remains on the battlefield but loses its ability to deal combat damage (Rule 410.1.b / Rule 423.1.b).
2. Combat Damage Step: When the showdown proceeds to the damage step, you (the defender) assign damage to the attacker. Because the attacker is stunned, it cannot deal damage back to your units.
3. Killing: If you assign damage equal to or greater than the attacker's might, the attacker is killed and sent to the trash (Rule 428.1.a.2).

Important Note on Combat Resolution: If you stun the attacker but do not deal enough damage to kill it, and both your unit and the stunned attacker remain on the battlefield after combat damage is assigned, the attacker will be recalled to its controller's base during the combat cleanup (per RiftJudge FAQ 7095).