Love the different answers...no I don't clean up, but envy those with neat workspaces all the time.
One thing I do is trim small scraps to the nearest half inch in width. For example: quilt back trimmings will become an even width of a long length or when cutting squares from say a 2 1/2" wof, that bit of leftover is trimmed to a 1, 1 1/4 or 1 1/2" piece and gets tossed in its appropriate sized bin. Then when I I'm scrapping those sizes, they are my precuts...