[quote=@Raineh Daze]
<Snipped quote by IncredibleBee>

But whilst it can simultaneously cut two separate things, the different parts would be supporting one another--you can't cut the magic unless you can cut the physical, and you can't cut the physical unless you can cut the magic. If the magic simply amplifies the physical effects, you can't cut either, and you'd get a stalemate.
[/quote]

If the antimagic effect is engaged by cutting stuff, then the Dragonslayer is attacking both the magic and the physical at the same time. Thus, both items collapse simultaneously. It's like a door that's opened by two button presses at the same time.