You send notice of appeal to appeal it. Send it certified mail, r.r.r. so you have proof of the SSA's receipt. They may have told you to send an SSA-561 or HA-501. But yes, APPEAL and in that cover letter, specify that she wishes that her benefits CONTINUE pending the appeal.
Now, you indicate that it is your mom's SS business and not yours. This means, typically, that SSA will not work with you and you have no standing. But, if you get your mom to sign a SSA-1696, ASAP, and you fill it out and sign it also, you can be her appointed representative and SSA MUST work with you on her behalf.
Once she appeals (or you do it as her rep), at some point, if not corrected before then, it goes to ALJ hearing and the ALJ when he decides the "answer" will have to fully document with evidence and law, how he came to his decision. But I think this should resolve before then. As her rep, you can also ask for a complete copy of her SS file/folder on CD - and in there you should find all the chit chat behind the scenes that led to this horror show.
Even though you are appealing, you can also try your Congressman - explain that they have cut her benefit but NOT given her a reason, that you are appealing, but you wan't the details so you know what you are appealing OR you want it fixed right away. Can't hurt. But DON'T neglect to appeal timely, and with PROOF that you got it in on time.