My husband kept cutting off the beveled edges to make easier measurements. I suggested only cutting one edge where possible. Also he was cutting the off side (brown) and leaving roygh paper edges. I also suggested cutting good side. Maybe I should've been a little more forceful with my suggestions in the first place. Can two rough edges be joined without an obvious bump under mud?
Yes, but it depends on the skill of the taper. (Some drywall hangers only cut one side of the sheet and literally break the other paper face with a violent snap.) Slightly ragged cuts are not a concern, as they'll be moistened when joint compound is applied and flattened when paper tape is pressed on.
If you're truly concerned about certain areas, take a utility knife with a new blade and slide it along the joint at a 45 degree angle, shaving off the edge of the paper along the cut.