Can we have the secretary of state cancel deceased mother's drivers license so no one can use her ID?

I agree with notifying everyone she ever did business with. DMV, voter registration, credit cards, membership in organizations, double check with SS, visit medicare to ensure the government did its job, any and all insurances ( health, life, auto, home owners,).
I spent over a week after Luz (DW) passed running around to ensure all of her accounts were closed. The worst was auto insurance and utilities.
don't forget her doctors, etc.
Cutting things up does not destroy records held by others.

Does someone in the family have a copy of her driver's license?

Rreport the theft to the police. Send the police report to the DMV along with the death certificate. This is identity theft waiting to happen.

Make sure all 3 credit bureaus know that she is deceased as well.

I second contact DMV

Go to the DMV site. They want you to send a copy of the death certificate and the driver's license to them. Do so. I actually sent a copy though they asked for an original. They were fine with the copy. Then send a letter to all the credit reporting agencies (I only sent to one as it is said one tells the other two). Again, send a copy of the death certificate. An example letter is online what to say but basically that the person expired and not to issue any credit in their name. I got a nice letter back from Experian. Then call Social Security. Normally the funeral home does this. This is a VERY GOOD IDEA to prevent fraud. Be certain that all credit card are called; the number is on the card.

Why not just cut it up and throw it in the trash? The state has already been notified of her death....