Hi Colin,
As far as I'm aware, it's the garlic that is oxidising. I am not aware of it causing any particular problems.
Try covering it (i.e. excluding the air)...or, as others have suggested, adding oil (rather than water) to it, when you mince it.
I mince mine, with water, and freeze it in ice cube containers...then into sealable sandwich bags. No problems at all. But I do notice it will go blue if defrosted and left sitting around for a while (e.g. hours).