You can file a lawsuit for any reason at any time. It doesn't mean it will get you anywhere. Most frivolous lawsuits -- and I do mean most, like 99.9% of them -- get tossed before a deposition is even taken.
Slander, or libel, requires YOU to prove that what she said about you is NOT true. In other words, she says you stole $40. You need to prove that you didn't, she doesn't need to prove that you did. You also need to prove that her accusing you thus has damaged you in some real, tangible way, not just that it hurt your feelings.
So what damages have you sustained by her accusing you of stealing $40? Did she tell the whole world you stole $40 and now you can't get a job? You would have to prove that. There's really only one way to do that. You would have to prove that every employer from whom you sought employment didn't hire you specifically because your boss told them you stole $40. In reality, there might be 10,000 reasons why a future employer refused to hire you, none of which has to do with an accusation of a $40 theft. It's almost impossible to prove.
Now let's say you file a lawsuit and it actually doesn't get dismissed by a judge for being a frivolous suit. You will spend upwards of $250,000 getting to court. You don't have to hire a lawyer, but you do have to pay your own costs all the way through. You will have to go to court multiple times for multiple motions before you even get to the deposition stage.
You will have to conduct discovery, and you will have to have a whole mess of depositions, and depos cost upwards of $5000 each because the people who show up still get to get paid, like the court reporter and videographer, and we are not negotiable. You don't just get to skip depos beacuse they're expensive. Even if YOU wanted to skip depos, I guarantee you that Subways won't. Subways' lawyers will be deployed, and you can bet they will spend you into oblivion just by following the law.
Here's the thing: Judges can't award principle of the thing. They can only award what you have actually financially lost. You must prove that you actually financially lost something, not that you were merely inconvenienced or your feelings were hurt. You're going to have to prove this to either a judge or a jury. And if you can't, you're sunk and way deep in debt.
Let me give you some advice: Don't get so wrapped up in your own offense that you shoot yourself in the foot.
If you took the $40, give it back. If you didn't, she still has a good reason for accusing you thus. Bort is right. If she is accusing you, it's because the $40 went missing on your shift. Whether you took the $40 or not is incidental. You are responsible for the register. That means you are responsible for the $40.