I have some pieces that look like that left over from fussy cutting or clothing. I just leave it because I don't know what I will do next. Sometimes they are perfect for paper piecing.

Not only do I leave those odd cuts on the main piece, I also fold any small scraps of the same fabric inside. I have no small scrap heap.

Looks like my fabric. I'll cut each piece to the shape I need it when I need it. I never know if I will use it for an applique piece, something for a baby's clothing or a piece for a quilt. If I cut it straight across it would probably be just enough to prevent me from being able to cut out a small shirt or a long stem or leaf. Where's the fun in having everything cut into squares or rectangles?

I tend to neaten mine unless the odd shape is at the fold. Those I leave because the piece when opened up can be big enough to cut a shape out of.

A lot of mine looks like that when I have been paper piecing. I just cut out the fabric I need to fit the piece I need - it's not neat. :-(

I don't trim anything away after cutting a piece out of something or when making clothes. I save the little scraps too. No it doesn't bother me. The next time I need that fabric I just repress all the pieces and then use the one that works for the currant project. I call it tightening the belt.

I had asked on another post if buyers preferred the pieces "tidied up" - with a nice even edge - which I agree looks ever so much neater -

or

Whether they would like "the extra" left on.

Of the people that responded, most preferred to have "the extra" left on.

I decided - in many cases - to leave it on - and the buyer could tidy up the pieces if it bothered them.

I frequently cut fabric from the back side because it's easier to see the grain lines from the back.

Nope. That's how I cut mine.

Looks like my scraps! I never trim off the pointy bits because I'd hate to have the perfect fabric for a certain piece only to find out that there isn't quite enough. Those messy peaks and points have saved my butt more than once.

Looks like mine, too. If I were to trim off the odd parts, that would be exactly how much more I'd need for the next cut to fit. I've never been the obsessive-compulsive type, though; just happily go with the flow. :D