It’s not really a perspective - you If you remove a single line, like this:
The circle on the left is still closed, but the one on the right is now just an arc. The trim tool intentionally leaves it this way. It’s a tool used for shape editing, meant to be similar to scissors in other applications.
If what you truly wanted as a result was a closed shape with a cutout, then the Boolean difference tool would be the correct tool for that task.