Mom scammed financially. Any advice?

Let's start with "mom is of sound mind". No, she's not. She's cognitively impaired. Her judgement and reasoning ability is gone. Have you called the cops? You can't reason with a person with dementia.

Agree with Ba8alou, mom is not rowing with both oars. Pursue Guardianship for her and DO report the scam to police and her state attorney general's office. You and sis agree on who will be the Guardian and see a lawyer.
Then you check her bills to see if she is paying them
And you count her pills to see if she is taking them
Guaranteed you find rotten food in the bottom rear of the fridge.

I agree that mom is cognitively impaired, most likely Dementia. My father too, was hooked by a scam to release $250,000,000.00
But there is another dimension to the scam, the scammers spend months gaining their trust, charming information out of them, and creating the intimate relationship that is missing (scammer is usually the opposite sex).
The effect of this seduction makes them easily pliable, because the elder does not want to lose this connection, it would be a death of the most emotional supportive relationship they have ever had, sometimes for many years. Makes sense?
So, you have limited choices on how you can end this relationship. You can stop focusing on their money, and let the scammers take it all. When the money is gone, they end the relationship. Of course, your loved one is now emotionally and financially devastated:(
The other, is to sacrifice your time and money to intervene, like they are the child, never to really be left unattended ( in the most subtle way of course). This is difficult, you have to move in, or move close. You need to set up "help" to keep someone coming in and interacting with her. These can be home health aide medical checks, house cleaner, visiting nurse, friendly neighbor, and of course you! You taking her out to lunch, hair styling, cute little shop that just opened up, etc.
You will also have to take control of services that provide an avenue for the crooks. Charter Cable is the only phone provider I know that has the will to use software to block all incoming and outgoing international calls, 900/976 and 800 calls. You could research other options in your mother's area. If you go the Charter option, do their cable too, blocking all ordering capabilities, and channels that promote selling. People with brain disorders, like dementia should not have access to a computer, there is no way to block criminals completely, as they are always creating new paths to steal money and identity. If you live there, just have WiFi set up, and always keep your computer locked.
Just think of everything as "how do I protect my 12 year old", and put those protocols in place. All monthly bills should be on auto pay, credit cards should have fraud alerts, be frozen, or, in my opinion, closed. You will need a durable power of attorney for this.
At this point, I have to ask, is all her real property in a Trust? It should be, with you and siblings as successor trustees. This is the only way, upon her death, to avoid probate and the lawyers/courts hefty cost. Items in the trust would be house, car, anything that would go through probate. She should have a Living Will that includes a Medical POA, so in the event she is unable (like a massive stroke) she is unable to make a decision, her loved ones can. She also needs a Durable POA, for situations like the one you are in now, or one like the massive stroke, so you can take care of her responsibilities and needs when she no longer can.

Well, there are your choices. If she did not prepare for this stage of her life, or is resistant to any interference, this all will be very difficult. This was the case with my father, but which ever sibling gets the best results "parenting" them, they should continue to built up trust, so your mother can lean on them, and rely on them, just as you relied on her when you were little!

God bless, and good luck!

Dr. Phil has had many shows regarding the *catfish* type that get the widow or widower emotionally hooked, sending photos of themselves [which are photos of someone pulled from a Facebook account thus taking on that Facebook person's identity], and promising these lonely people the world, but the catfish needs money for their work, money to fly in to see them [always living in another country for work, but at the zero hour cannot fly to the State for whatever reason], money for rent or groceries because their own money is tied up, etc].

What is so sad is the guest on Dr. Phil still believe the people they had been communicating with are real even with proof that *person* is a scammer.

Don't know if watching the reruns on one's computer from the Dr. Phil website would be of any help to your loved ones. Worth a try.