I keep small pieces together - either by color, theme, or type of fabric.
Woven plaids are kept together and so are batiks.
They are washed and ironed and kept fairly flat in small totes.
They usually are "dumped" when I am looking for something. Then I need to put them back into their container.
I enjoy cutting for a particular project.
The short answer is - No, I do not cut scraps into smaller pieces until I have something in mind for them.