There is a part of us that always want are art to be nothing shy of perfection. And when it is not many people seam inclined to immediately discard them. Though it is natural to be a critic of your work, I don't think it helps your growth and perspective as an artist to toss your work away even if you don't like the results. Because if you get rid of it how will you learn from it?

The saying "out of sight out of Mind" I think fits the bill here. If you throw your mistakes away then you wouldn't know what you’re trying to do. What causes your skin to craw when you observe it? How would you fix it? What aspects surprise you? Even if it's past a point of repair you can jot some notes down for reference.

Also it helps break a bad habit with materials. I remember a friend commenting on ripping the first page of his sketchbook out till he produced a good image. What a waste of paper. Rather than constantly slaving over the starting page you could work on you quality, values, style, and most importantly your mistakes. Plus it can be both satisfying and humbling to look through some older sketchbooks and see the progress you have made.

So try keeping some scrapes around long enough to make some discovery before you toss them out.