With an individual stamp, it works well by just running the Quick Selection Tool around the edges of the canvas. With the black selected, just Delete and I'm done. Is there any way to script this kind of action so it can be batch processed for 1000 stamps??
You could also try using a key color and key it out - like blue or green or pink or red or orange. I'd use a solid color piece of construction paper or felt on your scanner (I use black to scan type from magazines and newspapers so I don't get bleed through the back). In that case, you may get some bleed through the scans.
Along those same lines, try using Select > Color Range and use your key color - black is a common stamp color, though so it's gonna be difficult to automate. I think automating the process would require some large-scale intelligence in the script which I'm not qualified to code.
Incidentally, I have thousands of stamps from all over the world from a year ago so I'll see if I can try a few things later today.
I was able to solve my problem with some help from a poster in the After Effects forum.
If anyone is curious, the solution was to add the Paint Bucket effect to an adjustment layer, with the coordinate set to the top left corner, and fill in 100% red. Then just key out red. I rendered out a png sequence, and automated a Trim & Save action in Photoshop to crop all of my stamps.