Replacing Awkwardly Cut Drywall
Cut 3/4 inches over each stud. (Oscillating multitool is the best for this, but patience and a utility knife will suffice.)

Screw new drywall on. You could use a thin bit of plywood at the top horizontal seam to stiffen it up. Screw the old drywall as well. (Be careful about the power wires.) Tape and skim the seams. Caulk the joint between the baseboard and drywall. (Texture? I can't tell from the pic.) Paint.