I agree, to get the best quality cut using a saw, it is ideal to support the work on a sacrificial surface. It is also important to press some scrap against the work where the cut will end.
When I make the first long trim cut on a fresh sheet, I save that scrap. Usually the end of that trim cut will eventually also be scrap, but if not a scrap piece is pressed against the work there to prevent tear out. The trim scrap becomes the backer for all the other cuts in that sheet.
This tear out is less of a problem when using a slider or beam saw with a scoring blade. Still nearly always when cutting sheet material on a slider saw I use a piece of scrap behind the work.