Time for a few clarifications, if you would? Are you replacing the existing baseboard for some reason? If so, are you concerned with the paper tearing and wall damage above the baseboard area, or are you planning on repairing the wall and repainting right down to the floor?
Now here is what I get from the pic. You are dealing with fully glued baseboard attached to standard issue drywall. Typically the reason it is glued, instead of the more typical installation using finish nails, is that the framing is done with light gauge steel studs, which are extremely common in basement build outs. The issue of wall damage is easily resolved, when removing baseboard, by using a utility knife to score the wall at the top of the baseboard. Once you get a piece to start peeling off the wall, pull with one hand, and use a putty knife to scrape into the gap, cutting the paper. This may limit severe damage, like pulling big chunks of drywall out. When putting new pieces up, either use taller ones to cover the damage, or use spacers to slightly elevate standard size (3-1/4") base, to hide the damage. Prime the damaged areas with Binn, or similar, and use cove base adhesive, spread with a notched trowel, on the back of the baseboard.
