I've been told that the developers never intended for this to be a part of the game, but you can scuttle neutral mines. Personally, I like what this does to the game. It adds a whole new dimension to Vasari.
TEC and Advent tend to only have access to a few neutral mines that are close by because their colonizer has to actually make it there. Vasari, however, use scouts that have no problem getting to mines on the other side of the map, so this brings new strategic elements.
Early game Vasari can have 10+ neutral mines on a random map and just go to town with the monstrous economy. What I've come to enjoy doing is if I'm Vasari and I see that my enemy is moving for a neutral mine that I took in his territory, I'll scuttle it. Good players understand the huge impact neutrals can have on gameplay b/c the impact of them on early game economies is huge, and great in later economies.
Scuttling a neutral may seem like a bad idea, but if it's in enemy territory, that means your enemy is the most likely to keep that mine. You may get it everyonce in a while, but you can't waste your time keeping after that. Just scuttle it and hurt their eco. 