/diy/ - Do It Yourself

Is there a way to cut the bottom out of a jar or bottle, and still be able to glue the end piece back into place?
Not slicing the entire bottom off, but... I guess coring it? Pic related, cutting out where the red line is, then gluing it into place when I'm finished putting stuff in the bottle.

Slicing the bottom and gluing it back into place would be far too obvious and ugly for what I want.
If it can't be done, it's no big deal.