I'm a relative newcomer to the craft, but have found that for some reason, I cannot bring myself to throw away the offcuts - even to the small size of 1.75" x 1" scraps.
I've even kept ripped strips 'just in case'

How small are your scraps before you consider them of no further use??

Miniature quilts use tiny scraps, threads can be thrown outside for the birds to use in their nests so. . . . .

A lot of depends on just how frugal you want to be or how much you want to challenge yourself.

I am saving my tiny strips and torn strips to braid together and make mini braided rugs. Not sure what I am going to do with them after that - don't own a doll house to use them in, but maybe by the time I make a few an idea will come to me.
Tiny pieces also can be used to make book marks, greeting cards etc. I save them all.

They can always be used as coasters or trivets.

A friend saves those little tiny dog ears you snip off triangles and fills jars with them.

There's also a technique called snippets that uses tiny scraps.

Not being all that good with little pieces I save those for stuffing my pillows. They are always going flat lol.

Oh my the fabric can never be too small. Especially if we are talking cotton fabric. It is perfect at smaller sizes to use as stuffing or put it on a window ledge and let nature make a nest out of it.

Use those torn skinny strips to tie to gift bags. Really cute.

I only throw away the tiny, tiny strips(more or less, just strings). The small pieces I save and will make a crumb quilt, the tiny strips I save, because I have instructions for making fabric beads, which I'll also do someday, when I don't have anything else to do. LOL

If I can cut an inch strip out of it, I'll save it. I cut all my scraps into squares and strips and I have a box of 1" (as well as other sizes) that I'm going to make tiny log cabin blocks with. My friend made a wall hanging and bordered it with these 1" log cabin blocks and it's so cute!