Cut by laying the framing square flat on the ceiling parallel to the area to be trimmed away and drawing the blade of your utility knife straight down along its edge, making a clean, shallow cut in the solid material. Pic 1.

Support the piece being cut away with your free hand, deepening the cuts until you have cut completely through and the damaged piece can be removed. Pic 2.

There might still be old drywall nails or screws holding damaged pieces to the side rafters; you might need to break the old pieces away.