Can you remove your embroidery stitches and start over? Yes!
If you're limited on supplies, make a mistake, and/or don't want to be wasteful, you can absolutely remove your embroidery stitches from a hoop and start over.
I often do this because I make a lot of tutorial videos that could be seen as "wasteful," given that they're largely meant to be demonstrations (vs. finished pieces of work); to minimize that waste, I will often unpick my stitches and use the hoop for another project.
If this is something you anticipate potentially needing to do yourself, there are a few caveats to keep in mind:
Make sure you're using fabric that has the ability to somewhat "heal" itself. By this, I mean that you'll be able to rub the fabric with either a pair of tweezers or the blunt side of a needle to fix the weave of the fabric where your original stitches were laid down - this way, you won't end up with a blank hoop that has a ton of visible holes where those original stitches were made. I tend to use linen and linen blends, which are super forgiving in this way. If you're using another type of fabric, the easiest way to see if it will heal itself is to... poke a hole through it before you get started and see if you can "fix" the hole.
When transferring a design or pattern, keep in mind that some transfer methods can be removed (e.g., heat- and water-erasable pens), whereas others may not be easily removed (e.g., pencil marks). I've written about different transfer methods in another post.
Get yourself a seam ripper - these are often used when sewing with a machine, but can also be incredibly useful when unpicking an embroidery design. Embroidery scissors can also be helpful, but having a super sharp tool like a seam ripper can make this process go by much more quickly.
Tweezers are your new best friend. They'll help you grab those itty bitty pieces of floss and pull them out of your fabric when your fingers can't quite get a grip.
I made a video to demonstrate how I do this with my own hoops, which you can watch below (or by visiting my Instagram page).