First off, do not use sand paper.
The sandpaper grit will wear off over use (which is it's function) and possibly remain in the dough.
You don't want anyone eating sand paper grit, and I'm not even sure what it would do.
It might even be a hospital-level problem if the grit gets embedded in any digestive tract tissues and causes inflammation.
Ugg.
Please don't.
If you have a mandolin slicer and the cookies are soft enough, you could set it up on a very thin setting and slide the cookies across the bottom, shaving off a tiny bit.
I like the sandwich idea above.
cooking.stackexchange.com/users/25282/Grey Dog
I'd take a different approach entirely.
Throw out the cookies, or at least don't eat them.
Compost them, or build a cookie fort for small mammals, or make something decorative, or play cookie frisbee (probably outdoors).
Use your imagination.
Consider this failure a learning experience – remember to actually learn from it – and try again.
cooking.stackexchange.com/users/680/Matt Ball
Take a sharp knife and scrape it off.
cooking.stackexchange.com/users/27121/Tanya C
Easy: cheese grater.
Cleans off the bottoms flawlessly!
cooking.stackexchange.com/users/53280/Atsuki
do what you would do with sand paper but with the edge of a blade at 90°.
i sometimes do that in toasts.
EDIT: agree with both comments below :)
cooking.stackexchange.com/users/27247/Alban Lusitanae
Place the cookies in an airtight tupperware container with several slices of bread spread over them.
The cookies will suck the moisture from the bread and soften up.
The time it will take to work can be anywhere from an afternoon, or overnight.
It just depends on how hard the cookies are.
I usually do this with just one or two slices of bread to keep cookies from going stale.
But I have managed to save some dry cookies by using more bread slices.
I can't say it will do anything for the burnt taste, but at least you'll be able to either chew them (or cut the bottoms off).
cooking.stackexchange.com/users/27280/Matt S.
When that happens with toast I just use a dull knife to scrap the burnt part off.
The thing about baking is most items are to be baked in the middle of the even
so there is even heat all around.
When there are two items on the same shelf just space them equally.
Another thing is to not oil the cookie sheet when baking.
Breads need spray coatings but cookies do not.
cooking.stackexchange.com/users/24151/ethalfrida
If you really do not want to toss them, use a clean brick-stone and use as if it were sandpaper.
:-)But not many people have those laying around...
Sandwich idea could work, also like the experience idea and tossing them.
You could always tell your friends that there is hasj stuck to the bottom! :P
cooking.stackexchange.com/users/27276/Remy van Tour
I made Cookies and they are burned at the bottom.  What can I do to remove the burned layer without destroying the cookies and keeping as much as possible from the good parts?  I was thinking of sand paper but I fear this leaves a taste from the "sand" and may be even not healthy.
Burned Cookies - Now what?
cooking.stackexchange.com
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cooking.stackexchange.com/questions/47289
cooking.stackexchange.com/users/11353/juergen d
Do not use sandpaper, as some of the grit will wear off and remain in the dough. Instead use a mandolin, cheese grater, dull knife or even a clean brick stone to remove the bottom layer, or just throw them out or use them for something decorative. Many kitchen utensils can be used to scrape burnt parts off food, for example a mandolin or knife. Burnt food can also be used as compost or maybe it should just be thrown away.
Do not use sand paper to remove burnt parts on food. Mandolins, sharp knives, clean brick and cheese grater can be used to remove burnt parts on food. Throw the cookies away or use them as compost or something else useful.