What you're describing doesn't sound like sorting at all, but merely removing an element from a list while retaining the order of elements in the list. I would recommend using linked lists for that.
Yeah, linked lists is the standard solution for that in most programming languages. I don't know how they work in JASS, but C++ has awesome commands that make adding and removing things easily, similar to what you're doing.
Can I see an example? The one on wiki, I can't read...
I use it in the IDDS, which you can check if you'd like. These guys seem to know what they're talking about, though, so you probably don't actually need a sorting algorithm at all.