Yes, this is a very messy thing to do in your livingroom. Fortunatly the home we rent already has the most hideous carpet I've ever seen in one house. When the landlord asked if we wanted him to replace it, we declined. We would rather trash trashy carpet than have to spread tarps or whatever all over.
Our bank of grinding tools consists of the ring saw, large grinder with an ultrafine dichroic grinding bit, a small grinder with a standard bit, and a Covington wet belt sander.