I just tear away the big piece around the design--then press. If any inside pieces cause the fabric around the design to wrinkle I remove those inside pieces. H&*

I only remove the big peaces, Yvonne

It depends on the use. The excess stabilizer (where there are no stitches) will eventually come out in the wash. If it is to be sandwiched in a quilt, I use a cut-away stabilizer for dense designs.

I don't remove all the very little pieces. And I try to use black tear away on dark projects and the white on the light colored.***

I remove the big pieces....but sometimes spritz the little one if it is on something that needs to be removed but the water will get it out with a small tweezer point....

I don't bother unless the little bits will affect the appearance of the embroidery, as in where you'll see the back of it. Otherwise, they either disappear with use or help to keep the embroidery stable. Sometimes those little bits help to stop the embroidery from becoming distorted.
AlmaG.

I only remove the big outsides. Unless it affects the look of my embroidery.

As they say don't sweat the small stuff...lol. Even pre-embroidered clothing that we buy will usually still have some stablizer in them. So if it doesn't interfer in anyway with the design I just leave it.