Those look like some of the donated fabrics I get from someone taking a class & having to cut a weird shapes out!! I cut them straight across & do as you do put the rest in the scrap bin!

Whenever I cut appliques out, I leave my fabric like that. I never know what I'll cut out next, lol.

I am on the fence about this. I hate that look too but then again I have needed that little point to make enough room for a odd shaped piece so if I can fold it up and not have a big messy pile I leave it.

People do things differently. I like to keep my big pieces together, and cut all of the small pieces into bins using Bonnie Hunter's method for a guide. It is working for me. I usually cut off a small piece of my fabric when cutting out a project, depending of what I am doing, but I do find some like that, but later on they do get trimmed and later into proper bins. I am almost caught up with my scrap control on cotton. But still out of control on my flannel, but I am getting it organized slowly. When I get this done, my second goal will be to finish up all of my UFO's, so I can move on to other projects without all that clutter going on. Wish me luck!! HA HA HA

Those look like mine lol

ditto here

Thank you, nice to know it makes sense to others too!

That is exactly what my stuff looks like. LOL. Sorry. & some scraps are even pinned back to the main fabric.

?? I might need it?? Dunno. but no, I dont trim off the peaks.

cheep cheep cheep, I guess. :)

Back in the olden days (so I've been told) fabric was cut using scissors and templates. I imagine this would be the result. (Also with applique pieces being cut out.)

That fabric looks like it's been used for clothing.
I have trouble with that type of leavings, because it's hard to tell where the straight grain is and that's a problem if I don't want to use the bias.