" Is this possible"
Probably. That doesn't mean it will be simple...
Particularly the part about " start eating them" which is vague. If that's only removing some vertices from the polygon, it isn't hard, but if you plan to do it realistically, digging in the polygon, ie. making new vertices in a concave way, it is much harder...
Another way is to make composite polygons, made of several pre-made sub-polygons, removing them progressively...

Anyway, your goal is perhaps more ambitious than you expected...

Probably what I want is making a small 2D game in which some small circles like the red one start digging through the black polygon, just like the way in the digger game.