For a trap out, after all of the bees and the queen have absconed from the hive (at least 5 to 6 weeks) take the screen cone off and let them rob the honey out of the old hive. This should take about a week for them to clean it out. Then seal the entrance up with silicon caulk. Game over. The only thing left in the old hive will be the empty combs.
Now for a cut out, remove all of the comb and scrape it clean best as you can. I like to use fiberglass insulation to fill the void, replace the building materials (sheet rock, siding, paneling, etc.) and then seal with silicon caulk.